Travel between systems is split into two parts.
1) Hyperjump (from one system to the next)
2) Supercruise (rapid travel within a system)
As mentioned by ste you select your destination from the side menu. Once you have selected you destination (use your compass to find the correct vector - #6 in the below image) you engage your hyperjump (I
think that the default to engage is J).
You will exit hyperjump near a star. For now it is best to press X to stop your engines (later you will be able to do navigate to your final destination seamlessly) and then look at your navigation panel again. Lock on to your destination (which will most likely be a station) and then throttle up (default W). Again, look at your compass.
Now for the slightly tricky part - supercruise. You can watch
this tutorial from for more info.
To exit supercruise you should be within 1000km of your destination and then press J. If you are going too fast and you overshoot it's no problem, just loop back around to your destination (again, that compass is super handy) which will mean your speed will be constantly reducing speed (assuming you are slowing down in the first place

).