I own my place and want to rent a room to someone. Where can I turn to do a background check on someone to make sure their history is clean? Thank you.
If you are willing to pay for it, there are lots of web sites that will let you do a fairly detailed background check on anyone almost instantly. Otherwise, you can just snoop around on Facebook and Goggle their name although that is a little creepy.
Yes, much less creepy to run a detailed background check instead of Googling them. 
I’m a fan of asking questions based on the DSM. Example: Have you filed more than 3 lawsuits in the last 3 years? That tests for the presence of litigious paranoia (a real mental condition, I swear). Also, the question serves to screen out any lawyers.
I assume you are planning to run a credit check - this has been standard for all of the apartments I’ve rented. It’s customary (and possibly required) to inform people that you will be running a credit check. Also, I would do a reference check of the last 3 prior landlords. That way you can find out if they paid their rent on time or caused any problems. I think it’s typical to call the applicant’s employer and verify that the person is in fact employed there and to check how long they have worked there.
Put out an ad like this on craigslist and only the best of the best will apply:
ETA: some swear words in description
Well, you want a roommate that is mature, employed, quiet, not crazy, not a criminal, and doesn’t plan to have parties every night. You’ll need to screen for all those things. I see doing a quick google search on “roommate screening” will give you lots of good advice on this subject (including questions to ask).