How to grind dilithium
Read this first. Grinding dilithium is most likely a waste of time. Opening your wallet, buying Zen, and exchanging it for dilithium is the fastest way to get the dilithium you need for upgrades and fleet projects and reputation and fleet gear. Calculating an hourly wage based on the dil-zen exchange rate for your dilithium grinding activities will just make you sad because it'll likely be under $1/hour. Even the Voth BZ only rewards around $0.70/hour at the current exchange rate (assuming dailies and 2 decent runs in 1 hour).
If you make a daily routine of some things, across several characters and farming alts, a couple minutes here and a couple minutes there, the time adds up and pretty soon you're not playing the game anymore (at least not the game you signed up to play). There's nothing wrong with paying real-world money for dilithium; you're just paying for your entertainment, the same as when you buy a theater ticket or an album.
Of course, I don't follow this advice very well and that's how I learned all the stuff below.
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Getting dilithium in-game is 2 separate processes: 1) obtaining unrefined dilithium and 2) refining it (maximum 8000 dil/day). I divided this guide into those 2 parts.
Obtaining unrefined dilithium
1) Turning in contraband. Buy contraband on the exchange or earn it through doff projects, mostly marauding projects for KDF characters or "Confiscate contraband" and a few rarer projects for Feds. Turn it in at the security officer at Earth Space Dock, First City on Qonos, Ganalda, DSK7, SB39, or DS9 (there is no security officer at New Romulus). Get 2000 dilithium for several seconds of work if you park a character in front of a security officer and visit that character no more than once every 4 hours while you play other characters.
2) Turning in VIP dilithium claims (especially on a dilithium weekend). Get up to 5000 (10,000 on a dil weekend) for one of these, depending on your skill at the mining mini-game. These claims come from opening lockboxes and are bound-to-account, so you can't get them from the exchange.
3) The Voth Battlezone. This gives enormous amounts of dilithium compared to pretty much everything else in the game. I calculate on the linked thread that a good-but-not-great run will get you over 11,000 dilithium for 20-30 minutes of playing the game if it's your first run of the day. If you think the Voth BZ is hard, read the linked walk-through.
4) Mining dilithium - You get 5 sites/day at the Ferengi's Vlugta asteroid and 11 at the fleet's mining asteroid a day. 735 points or more gives 200 dilithium at normal mining sites and 480 at the Rich Dilithium site at the Fleet Mine, and getting over 735 does not give any more dilithium. You can earn up to 2480 for 20 to 30 minutes of mining, depending on your skill at the mini-game.
5) Going through elite ground missions (NTTE, DRSE, BHE, UIE, BOTSE, NSDTE). 6 elite ground PVE queues that aren't too hard if you have good ground gear and know the missions. You can try to put a tour together in the ground DPS channels (if you parse over 200 DPS in NTTE) or in the PublicEliteSTF channel or in the fleet's channel, or you can pug the first 5 listed above and usually succeed (NSDTE is harder). A good tour takes about an hour and will get you 8640 dilithium and a bunch of marks and elite marks (borg neural processors, etc) that you can exchange for more dilithium.
6) Admiralty - Admiralty projects can give up to 500 dilithium and events attached to those projects give 500, 1000, or 2000 dilithium. Look for these projects and skip/send shuttles on others if you want to grind dilithium this way. KDF Tour of Duty 10/10 gives 30,000 dilithium, is available to all factions, and is repeatable if you get through 1/10 to 9/10 again.
7) Turn in marks. Go to the Reputations tab, click on a reputation that you have more than 50 marks for, and find the "upgrade" projects that let you turn in 50 marks for 500 dil, 250 marks for 2500 dil, or 500 marks for 5000 dil. You can also turn in 3 elite marks (Voth Cybernetic Implants, etc.) for 1000 dil.
8) Visit the fleet research lab once a day and go to the development room. An NPC gives you a short R&D project that requires a few common and uncommon R&D materials and will reward you with 1200 dilithium, some rare and very rare materials, and 5000 bonus R&D XP.
9) Finish your reputations. Check in once a day and do the daily project for each reputation (340 dil/day) once your character is at level 50. Most of the reputations give 32,000 dilithium and a bunch of marks when you finish.
10) Just playing the game. There are lots of things that give dilithium (PVE queues, episodes, daily missions, doffing, battlezones...), but nothing else stands out as an efficient use of time to get dilithium. But if you're playing for fun, you can usually get some dilithium for what you're doing and that's nice too. Post other ideas if you know of something particularly efficient or fun that I didn't include.
Refining more than 8000 dilithium/day
1) Go to the fleet mine and talk to the Reman on the other side of the room from where you beam in. You can refine 500 dilithium this way once a day.
2) If you're an 800-day subscriber or have a lifetime subscription, visit the Veteran Miner at either academy to refine another 1000 dil in a 2-day doff project.
3) Play on other characters. You're limited to 8000 dilithium a day per character. I have a few characters that I enjoy playing and I try to lay off the characters that already have a lot of unrefined dilithium and play the ones that have little.
4) Farming alts. Like having more characters to play on, but this is when a character exists as nothing other than a source of dil for your account. Park this character in front of the security officer to turn in contraband, or maybe at the mines or the Voth BZ to run through those when you're bored on your actual characters. Maybe just set up admiralty and doffing every few days.
5) Play the dil-zen exchange. If you think you can predict the market, then buy dilithium with Zen when the exchange rate is high and buy Zen with dilithium when it's low. WARNING: This is a dangerous activity and you could lose a lot if you don't predict correctly where the market is going. Cryptic announces things every week that shake the market and you can't predict what they're going to announce, you can only try to react to it faster than other players. I am not responsible for any resources lost.
Passing dilithium between characters on an account
Go to the character who is giving the dilithium and open the dilithium exchange (Inventory>Assets>Dilithium Exchange). Create an order to buy dilithium. Set the price to something substantially below the current exchange rate but above 25 (the minimum). Enter the amount of dil you want to transfer. Go to the character who is to receive the dil and cancel the order and remove the dilithium from the market.
If you make a daily routine of some things, across several characters and farming alts, a couple minutes here and a couple minutes there, the time adds up and pretty soon you're not playing the game anymore (at least not the game you signed up to play). There's nothing wrong with paying real-world money for dilithium; you're just paying for your entertainment, the same as when you buy a theater ticket or an album.
Of course, I don't follow this advice very well and that's how I learned all the stuff below.
--------------------
Getting dilithium in-game is 2 separate processes: 1) obtaining unrefined dilithium and 2) refining it (maximum 8000 dil/day). I divided this guide into those 2 parts.
Obtaining unrefined dilithium
1) Turning in contraband. Buy contraband on the exchange or earn it through doff projects, mostly marauding projects for KDF characters or "Confiscate contraband" and a few rarer projects for Feds. Turn it in at the security officer at Earth Space Dock, First City on Qonos, Ganalda, DSK7, SB39, or DS9 (there is no security officer at New Romulus). Get 2000 dilithium for several seconds of work if you park a character in front of a security officer and visit that character no more than once every 4 hours while you play other characters.
2) Turning in VIP dilithium claims (especially on a dilithium weekend). Get up to 5000 (10,000 on a dil weekend) for one of these, depending on your skill at the mining mini-game. These claims come from opening lockboxes and are bound-to-account, so you can't get them from the exchange.
3) The Voth Battlezone. This gives enormous amounts of dilithium compared to pretty much everything else in the game. I calculate on the linked thread that a good-but-not-great run will get you over 11,000 dilithium for 20-30 minutes of playing the game if it's your first run of the day. If you think the Voth BZ is hard, read the linked walk-through.
4) Mining dilithium - You get 5 sites/day at the Ferengi's Vlugta asteroid and 11 at the fleet's mining asteroid a day. 735 points or more gives 200 dilithium at normal mining sites and 480 at the Rich Dilithium site at the Fleet Mine, and getting over 735 does not give any more dilithium. You can earn up to 2480 for 20 to 30 minutes of mining, depending on your skill at the mini-game.
5) Going through elite ground missions (NTTE, DRSE, BHE, UIE, BOTSE, NSDTE). 6 elite ground PVE queues that aren't too hard if you have good ground gear and know the missions. You can try to put a tour together in the ground DPS channels (if you parse over 200 DPS in NTTE) or in the PublicEliteSTF channel or in the fleet's channel, or you can pug the first 5 listed above and usually succeed (NSDTE is harder). A good tour takes about an hour and will get you 8640 dilithium and a bunch of marks and elite marks (borg neural processors, etc) that you can exchange for more dilithium.
6) Admiralty - Admiralty projects can give up to 500 dilithium and events attached to those projects give 500, 1000, or 2000 dilithium. Look for these projects and skip/send shuttles on others if you want to grind dilithium this way. KDF Tour of Duty 10/10 gives 30,000 dilithium, is available to all factions, and is repeatable if you get through 1/10 to 9/10 again.
7) Turn in marks. Go to the Reputations tab, click on a reputation that you have more than 50 marks for, and find the "upgrade" projects that let you turn in 50 marks for 500 dil, 250 marks for 2500 dil, or 500 marks for 5000 dil. You can also turn in 3 elite marks (Voth Cybernetic Implants, etc.) for 1000 dil.
8) Visit the fleet research lab once a day and go to the development room. An NPC gives you a short R&D project that requires a few common and uncommon R&D materials and will reward you with 1200 dilithium, some rare and very rare materials, and 5000 bonus R&D XP.
9) Finish your reputations. Check in once a day and do the daily project for each reputation (340 dil/day) once your character is at level 50. Most of the reputations give 32,000 dilithium and a bunch of marks when you finish.
10) Just playing the game. There are lots of things that give dilithium (PVE queues, episodes, daily missions, doffing, battlezones...), but nothing else stands out as an efficient use of time to get dilithium. But if you're playing for fun, you can usually get some dilithium for what you're doing and that's nice too. Post other ideas if you know of something particularly efficient or fun that I didn't include.
Refining more than 8000 dilithium/day
1) Go to the fleet mine and talk to the Reman on the other side of the room from where you beam in. You can refine 500 dilithium this way once a day.
2) If you're an 800-day subscriber or have a lifetime subscription, visit the Veteran Miner at either academy to refine another 1000 dil in a 2-day doff project.
3) Play on other characters. You're limited to 8000 dilithium a day per character. I have a few characters that I enjoy playing and I try to lay off the characters that already have a lot of unrefined dilithium and play the ones that have little.
4) Farming alts. Like having more characters to play on, but this is when a character exists as nothing other than a source of dil for your account. Park this character in front of the security officer to turn in contraband, or maybe at the mines or the Voth BZ to run through those when you're bored on your actual characters. Maybe just set up admiralty and doffing every few days.
5) Play the dil-zen exchange. If you think you can predict the market, then buy dilithium with Zen when the exchange rate is high and buy Zen with dilithium when it's low. WARNING: This is a dangerous activity and you could lose a lot if you don't predict correctly where the market is going. Cryptic announces things every week that shake the market and you can't predict what they're going to announce, you can only try to react to it faster than other players. I am not responsible for any resources lost.
Passing dilithium between characters on an account
Go to the character who is giving the dilithium and open the dilithium exchange (Inventory>Assets>Dilithium Exchange). Create an order to buy dilithium. Set the price to something substantially below the current exchange rate but above 25 (the minimum). Enter the amount of dil you want to transfer. Go to the character who is to receive the dil and cancel the order and remove the dilithium from the market.