In the lowest security areas, however, the 0.0, there isn't really such a thing as piracy at all, because anything goes. This is a free-for-all, and it's the area of space that players are able to lay claim to as their own. But more on that in a bit.
There are three lessons you must learn to make the most of your time in EVE. The first is that this is a game about human interaction. While there are missions you can do on your own, and ways of making money that do not require the help of other people, the only way to really make your way in the game is to have lots of human allies. This is not an ideal game for loners, or for soloists. If you follow the mission sequences that the game provides, it now offers you a way to find a wingman, and also to browse the corporations that are recruiting. The best corporations are generally invitation-only, but many starting corporations are there simply to help you out and to provide advice on how to do things like sorting out your overview or fitting ships. (EVE University, found at www.eve-ivy.com, is one such corporation, which essentially teaches its members how to fly in combat missions. Worth a look if you want some basic tuition.)
Fitting ships is the other thing you're going to have to get your head round to survive. This is the central art and science of flying in EVE. Every ship can be fitted in thousands of ways, and most of the ways that you can fit them are utterly terrible, and bound for failure. Understanding how to get the most out of a ship, and what modules are best installed on it, is something that you will have to take time, and advice, to master.
The basic principle is that you should play to a ship's bonuses. If you read the description (the little blue "i" or "show info" on the context menu) you'll see that every ship has a specific bonus. This will often simply be based on the related skill, meaning you'll want to train that skill up as high as possible to make the most of it, but it might also determine what bonuses you have to particular weapons or other modules. You'll want to play to a ship's strengths, but you'll also have anticipate that your enemies will probably have a good idea about how you're going to be fitted. While there's no perfect way of doing these things, being able to do something that your enemy doesn't quite expect will often result in a win.
Of course this ties into the other thing that you're going to have figure out: EVE's complex skill system. There are no classes and no levels in EVE, but as a character ages he accrues skills. You set a skill running and your character slowly learns it, with the speed dependent on his personal attributes (which can in turn be boosted by learning skills). Easy skills take just a few minutes to learn, while those which are required for the high-end toys can take weeks, even months. Learning to make the most of this system is one way in which you'll benefit from playing EVE. If I have to take a month out of the game to work I can set a long skill training and have a far more powerful character when I return - even though I've not been able to play.
Finally, you need to set yourself some goals. You're probably going to want to have a couple of different ship types at your disposal. For your initial weeks an assault frigate should give you something to work towards that you can easily complete missions with. As you find a corporation and start to work with them it'll become clearer what it is that you want your character to do. Perhaps he's going to be an elite scout, such as a speedy interceptor, or an invisible covert-ops. In time, perhaps both. There's an enormous range of possible futures for any particular EVE pilot. Some will specialise in mining and refining and use their time to quietly gather resources for a corporation, paying for ships and providing raw materials for ship building. Others might become the dreadnought-flying siege masters, who knock over the enemy towers which stake sovereignty in the depths of space. Others still become masters of speedy flight - raiders and guerilla warriors who make a living from hit-and-run.
No other gaming universe can claim EVE's achievements, nor can they command your complete attention in the way that EVE does. In EVE you're sinking time into something that is growing, evolving and changing with the players in there. With the help of other players you'll be able to build structures which will be there until that far off day when the game ends and the servers shut down. You'll be able to add to the legend of corporations, to genuinely defeat your enemies and destroy their most prized ships. If you want to leave a mark on a game, then this is the place to do it.