If you want to be eased into things, you can join EVE University. They'll pay for all of your skillbook trainings, and they're also really good at teaching you how to operate in a fleet and follow wartime operations. They area also, however, very very strict, and if you don't like being told what to do then this is not for you.
If you want to do combat, which I highly suggest, you can join faction warfare, or join a wartime corp and help in their operations. Or join Red vs Blue and have fun blowing each other up. Best advice I can give for combat is to fly without fear. Understand that everything you fly is going to get blown up, it's just a matter of when.