Buy/Sell: Well, you need money for this, and more than the amount you start out with. It helps to have over 100K. You'll want to have ~2mil for a fast ship, though you can get cheaper ones in the hundred thousands. Best way to do this is to get more credits, of course. So..
Getting more credits: Join a faction! Factions pay you salary and assign you a ship to use. If they're worth anything they will of course take you to the ship, as well. (:
Find Civilization: There are cities on many planets in the galaxy, but you can't really do anything on the surface. The cities mostly exist so producers have factories to build in, and governments/people have facilities to get some income from.
Fight: Actual combat is not yet implemented. Many factions already train and gain XP to prepare for combat, since each time you level you can allocate more skill points, and the higher you are when combat is out, the more of an advantage you will have. People can die through the arrest/execute feature, but this doesn't use skills and only faction members with proper privileges can use this (and then, in most cases, only on faction members).
Fly: You need a ship for this. As I mentioned, your faction should assign you a ship and bring you to it, then you will have options on your right menu which will allow you to fly.. Particularly, the "enter cockpit" link when you're in the cockpit room on board your ship. (: