Hello, commander and welcome to the Big Black.
A couple more questions:
Which training mission?
Is it just forward, or are you unable to move at all (rotation, lateral thrusters)
Are you floating in space? In that case you probably don't have the controls configured. Go to the control options and try resetting to default with your controller. If it doesn't help check the "Flight throttle" section to find out whether everything is bound, then do the same for Rotations and thrust.
Or are you docked at the station? It that case you might just overlooked a Launch button in the middle of the HUD. Or maybe you have pressed it and flight checklist appeared on the top right. It that case you have to "check" all the tick-boxes by performing the required flight control operations.
If it isn't any of these, you'll have to give us more details, I'm afraid. Good luck for now!
Also, there is a dedicated
Xbox section, here on the forums. I'm not saying you're in the wrong place for newcomer help, quite the opposite and we will try to advise you to the last breath, but if your problem is somewhat tied to the controller, for example, the guys over there may be able to troubleshoot you more quickly.