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The player guide tells you the commands, but here is some of the list with an expanded explanation:

Space - FIRE!

W, A, D - Thrust / turn. Star Sonata works with inertia, which means your ship doesn't have brakes, and the only thing stopping you traveling in a direction is an opposite thrust. So, to stop you must apply a thrust against the direction you are traveling: this also factors in the weight of your ship, so the heavier you are, the more inertia you have. When trading, 500 microchips will effect you far less than 500 nuclear waste. Take time to learn how to use this against AI. Also note that all engines have both a thrust (how fast you reach full speed) and turn (obvious) stat, so choose an engine that best suits your ship: Traders will need high thrust to move heavy loads; combat ships need quick turning to target AI.

Tab, Ctrl, Q, Z - Next target, class of targets, cycle targets, closest ship. Learning to use Ctrl and then Q to quickly select your destination is very important and will save you a lot of time. There are two main advantages - each list is much smaller, and allows you to cycle quickly through them. Thus, if you are given directions to a system (usually in the form Sol - Crevice - Free Market and so on) you can select the worm hole class with Ctrl, and quickly cycle through to the named next system. There is also another advantage - when looking for missions, selecting the class AI station and cycling through them will give you an info tab (on the left, above the system map) that will tell you if there is a new mission there. Very useful to quickly check if there is a new mission!

V - autopilot. Essential. Note that at first you can only autopilot manually to the next wormhole. However, there is a skill, Astral Navigation, that allows you to set routes automatically, available at Earth Central, Sol. If you get this skill, each point allows you to set that many systems as a route by double clicking on the system in question on your system map. This is extremely useful for long haul trading - but be aware, you have to explore the systems first!

/ - select target / autopilot to point. Before you can shoot (space) anything you must select it with a left click. Likewise, if you wish to scoop something in particular, you must select it. Note that pressing C to scoop without targeting will scoop the closest thing if you can pick it up. This is useful for mass scooping a pile of debris, picking up the smaller items (for example Neural Keys) and leaving the heavier items. Right click will autopilot you to a destination, and bring you to a complete stop. Very useful for stopping yourself automatically at a point, especially on worm holes.