Just like in our real world, money makes EVE go 'round. It takes ISK to buy whatever it is you want - that shiny new faction frigate, the Tech 2 Ice Mining Barge, or a fully decked out SuperCapital. For many of us, PvP is the life and breadth of EVE - so ISK is gained by looting the wrecks of our victims and selling that loot on the market. But sometimes, lady luck shines elsewhere, and your coffers run dry and your ships get blown up faster than you can afford to replace them. Even with the recent "buff" to T2 insurance, you can't replace a Taranis hull (let alone the mods) with the insurance payout, so what's a poor PvP player to do for ISK generation?
The obvious thing is to run missions, right? Yawn. Sitting around for hours on end doing "target, orbit, shoot, loot, salvage, repeat" makes a dull EVE session. Well, there's market manipulation, right? Frankly, too much for me, shuttling around large quantities of item X from point A to point B - not the way I want to spend hours in EVE. Planetary Interaction (if you have the skills, time and no issues with repetitive stress injuries) will provide a thin income stream, especially if your Corp or Alliance is buying POS fuels at market rates. Not too hard to set up an Enriched Uranium chain, or Oxygen and Coolant. Ice mining earns decent money - if you have something else to do while your toon sits and cycles the lasers every 5 minutes.
The inventive (and amoral) character can scam their way into millions - just look at that Caldari Navy Raven sale via station trade...
But there is actually a fairly painless path to passive isk generation: Datacore farming. On your main toon, you might already have the basic skills in place - Science V? Now you just need to pick a Scientific field to study - I'd suggest looking at Datacore prices and picking the most profitable. I'm going to use Gallente Starship Engineering as my example, even though it isn't the most profitable. So you train up the specific skill to at least IV (assuming you have the prerequisites in place - usually one of these: Mechanic V, Electronics V, or Engineering V). Then you find who researches the field you want to farm - and go to the best agent you can in that field. Open a conversation, start research, and get on with your life. Once a month or so, go visit your agent, collect your datacores, and move them to a trade hub to sell for profit. Now this gets interesting with three character slots on your account - you can take the time to train up the basic skills for all of them and get at a Level 1 agent without any work - in about two weeks you will get about 10 RP a day, which isn't much (only about 1 datacore a week) - but that's an additional 200-300,000 isk a week that you don't need to do anything to earn – just leave that alt character alone, collecting RP for datacores while you fly your main. If you have the time, and energy, you really want to get to L3 or L4 research agents (I have a corpmate who gets over 200 million a week with 2 accounts/6 toons just doing datacores).
And yes, I profit from sharing this, since I have an R&D alt who does ship invention, and the more datacores out there the better the price on them for me to buy.