In 3D, before making a move, do you check the moving object against a list of all (n) collidable objects/surfaces (check if the new position is taken by any of them)?
Hi !
There are lots of ways to do this, a search on google gives a lot of “hits” 
BSP trees are often used for collision detection, a quick way to speed it up is to put a bounding box around each object and do a hit test on that first before you start doing collision detection on a lower level.
If you search this forum you will also find a lot of useful information about collision detection.
Mikael