You only need to download the 500MB+ Client from the EVE-Online -site http://www.eve-online.com/
at this moment it points to http://ccp.vo.llnwd.net/o2/EVE_Setup_25245.exe
) (fast download for a fast link, no 'long' patching). You can also access the download page at http://www.eve-online.com/download/
Then you get the CD-key from the first address. 14 days free game-time, no credit card needed for that.
Go through the tutorial (it takes about 1-2 hours), everything will be much clearer then. An easy game to get a hold of if you're a keen Elite -type fan. The first days were a bit "tedious" since you couldn't really fully grasp what's going on, however by just playing you get more and more interested in the game.
The tempo CAN feel a bit slow when doing long missions (many jumps), but luckily EVE runs on the background (you can still hear the computer tell you when it's finished jumping) and even works on this meager DELL Latitude D610 which I'm using (a laptop).