How do you get rid of house guests who refuse to leave?

I am especially curious about the legal situation. What if someone asks you to stay overnight because of an emergency and then, in spite of all discussion, negotiations and agreements, they keep on staying, making one excuse after another? You only let them stay one night...but they've extended their stay indefinitely. If you call the police, can you toss this person out? I've read about fired nannies and fired maids who stayed after being fired and then had to be legally evicted, a long, expensive process. Is it like that for unwanted house guests?