How long does this process usually take?

From the time you miss your first payment to the final foreclosure sale its not uncommon for six months or more to pass. In some state this could be more and in others considerably less. It will also depend a great deal on your mortgage holder and how aggressively they pursue your case.
When in the foreclosure process do I have to move out of my house?
YOU DON'T!!!!!!!!! The foreclosure process even when followed through to completion only transfers ownership of the house from you to the high bidder. This transfer of ownership becomes complete at a closing following the foreclosure auction. After the auction you automatically become a tenant in the house you formally owned. At this point the new owner must follow the legal procedures in your state for eviction.
What is the eviction process?