I'm through the academy and wondering what to do next to really get a handle on the game.
I would recommend looking around for some SOS signals and picking up some refugees to bring back to Sol for cash, assuming you have the fuel for it at least. It accomplishes several things: 1. It makes you some cash. 2. It allows you to explore the universe and fill out your star maps. 3. You should encounter a couple of the different SOS mission types in the game and get you more familiar with them.
Another good thing to do is find yourself a corp, they will often help out new folks by loaning them a much better ship than what you will have along with some fuel to help you get a lot of money much faster than you could on your own. There are several corps out there to choose from and I would say you should go through the corp recruitment thread to see if any of them sound like they would suit you.
Of course feel free to ask questions and look through everything here on the forums like Sargas said, the community here is very friendly and will be happy to answer any questions you might have. Enjoy your time here xD