Originally Posted by
dsbrantjr
To get the wheel fully and repeatably into the dropouts, hold the bike vertically with the wheel on the ground and press firmly down on the frame. Then secure the quick release. The quick release nut should be adjusted such that the lever takes considerable force to close; it should make a mark on your palm when you swing it closed. Having the wheel in a predictable position will ease further troubleshooting.
+1
Don't try to mount a bike wheel with the bike upside down. Be sure the axle is fully seated in the dropouts.
If fully seated and the rim wobbles the wheel needs to be trued and spokes tensioned. The rim should be centered relative to the axle lock nuts. The brake pads should then be centered relative to the rim, not the other way around.