Massively has posted an excellent article for those interested in trying out EVE Online that details exactly what you should do in order to get the most out of your free trial.
I've signed up for the EVE Online free trial program countless times now, and each time I've been faced with this massive universe of possibilities and absolutely no idea what I should be doing in it, which generally led to me wandering around for a few hours before giving up. Massively's Brendan Drain has written an extremely helpful article that goes over the various steps you should take in order to get the best feel for the game during that limited time.
Helpful hints included going with a combat profession instead of trying to get into trading and diplomacy within the span of 14 or 21 days, depending on where you get your trial, which is exactly what I had been doing wrong the past several times I tried to play. He walks you through attributes, professions, and even taking your ship to the next level.
I know there are other such articles out there, but this one came along at a time when I was really digging in and trying to find my way in the huge universe, and has helped immensely. I may still be lost in space, but now I'm lost in space with a strong sense of purpose!
EVE Evolved: Making the most of your EVE Online free trial [Massively]