What are the overall rules of Muktzeh and its categories?
When is one allowed to move a Muktza object and for what purpose?
An oversimplification, since that's what's being sought: Muktze is something (a) unusable, (b) valuable-cum-fragile, or (c) useless for non-m'lacha uses, or (d) a support for one of the above. Something useless or valuable-cum-fragile can't be moved or used. Something useless for non-m'lacha uses can be moved only if it's needed for a permitted use or occupying needed space. A support for muktze has the status of type of muktze on it. See one of the books mentioned in the comments on the question, or CYLOR, for details; certainly don't rely practically on anything in this answer.