Get references from past landlords. They can verify residency and on-time payments from your potential co-habitant.
Perform a credit check on the person. This should give you a good indication about the person’s ability to make bill payments, especially if you plan on sharing phone, cable or Internet services.
Spend a few hours with the person in a neutral location (like a coffee shop) and get to know one another’s interests, likes and dislikes.