Right-click on your Guildmaster (GM) and he will allow you to train up your skills. You only get 5 skill points per level, and although that doesn't seem like much many people barely spend any of them. In general they go up fast enough through use that you don't need to buy any, although you will need to spend at least one on certain skills that only become available at a certain level (for example, Dual Wield for Rangers at level 17 doesn't start working automatically, you have to put a point in it first). After you have 15 in a skill it starts costing money to train in it, although not very much at first. Finally, you can only train tradeskills up to 21, after that you have to earn the skills entirely.
Oh yeah, in order to see your skills open your inventory up, there is a Skills button on the bottom left. There might even be a way to open it without going into your inventory, check under Options/Keyboard/UI while in-game.