Hi Ted,
Generally speaking the trestle should have stayed attached to the keyboard and the key pops of that, in that case you inspect the bottom of the key and you should see that one end of the pivot points on the backside of the keycap is a snap in design and the other end is a slide on design.
Then proper refitting is to slide the slide on end of the key to locate on one end of the trestle and then fairly firmly push the key downward (as if you were trying to press it) until you hear a click or two.
If the trestle has come off with the key then that indicates that either the metal pivot points on the keyboard baseplate are bent or one of the the tiny pins on the bottom side of the trestle that locate in them has snapped off.
In the former case I would normally remove the trestle (carefully) from the key and then reattach it to the baseplate of the keyboard, maybe by gently bending the metal pivot points so it can go in and stay in. Then refitting the key in the above manner.
In the later case you are going to have to find another similar (but not necessarily identical) keyboard to be a donor for an intact trestle.
In terms of orientating the trestle there should be only one way it could sit where it will lay completely flat and yet still hinge upwards, that gets it the right way round front to back, so all you have to worry about then is if it is upside down or not...sometimes the fixings are the same top and bottom (on both the key and keyboard ends of each arm) in which case it won't matter if you get it upside down..other times the top fixing is either a different size or different layout on either the key or the keyboard (or both) in those cases it again should be reasonably obvious which way round it wants to go.
Sorry that would be a lot easier to explain in pictures or in situ.
If it helps then mark the trestle in respect to how it is orientated on the key it is attached to before removing it.
Regards Wayne