Massively

Tip #1: Go looking for fun:
Unlike the standard MMO norm, EVE doesn't have linear gameplay where you're led from one quest-giver to another and one region to the next. While this sandbox style is often touted as a good thing, not being led through the game is responsible for putting a lot of potential players off. With a game as complex as EVE, starting with very little direction can feel like being dropped in at the deep end. When given the choice of doing anything they want, new players can find themselves completely indecisive or afraid to do anything at all. EVE Online is a massive, complex game and you're free to explore any aspect of it. The flip-side to that is that the fun won't come to you if you just sit in a station all day or mine non-stop, you have to go actively looking for it.

The best way to combat the indecisiveness that all new players feel is to just pick something to do and try it out. If fighting NPCs in interesting combat scenarios sounds like your kind of thing, find an agent and try running some missions. If finding lucrative trade routes and playing the market sounds more fun, open the map and start travelling around the regions, looking at their markets as you go. If crafting and building ships, modules and ammo appeals to you more, blueprints and minerals are available on the market. No matter what direction you decide to take, however, your two biggest assets will be advice from other players and your own trial-and-error experiences.

Tip #2: Complete the tutorial:
We all hate to do tutorials and read manuals before playing a game but in a game like EVE, completing the tutorial can completely eliminate the hardest parts of the game's learning curve. CCP, the makers of EVE Online, have developers dedicated specifically to improving the in-game tutorials. Over the years, it's gone from being a quick in-space introduction on movement to a fun game experience that showcases a lot of what the game has to offer in a user-friendly manner. If you're still a little sketchy on some subjects after completing the tutorial, there is a wealth of player-made guides and tutorials available as well as an in-depth official player guide.

Although the EVE tutorial is quite long, it is highly recommended that you complete the entire thing. Not only will it eliminate a lot of the learning curve from being a new player but there are some nice rewards along the way to help new players get started financially. The new player experience is currently the focus of a lot of development at CCP, which promises to make the game much more accessible by the time the next major free expansion hits in March.