I recommend reading the FAQ, for those that haven't. After that, when you start, you begin at sector 0.
In the middle of the screen you can access the trading port or planet. The only thing you really need to focus on at first is the trading ports so you can raise a bit of money. Click on all the links on the left hand side to familiarize yourself with what they are.
On the right hand side you have your inventory and "realspace" and "warp" navigation controls. Warp is what you'll be using mostly. Each sector has a link to warp to another sector. Usually there's a way to go forward a sector and back a sector, and then often there's links to some other distant sector(s).
By moving with Warp, you only lose 1 turn on each jump. When you move via "realspace", you could lose hundreds of turns, so you use realspace travel sparingly. On the right menu, you can realspace travel to sector 0, where there's a spacestation. You can also set that panel to point to any other sector.
To start, you basically just warp to other sectors, and trade between them.
