Make sure your contractor is properly licensed
A license is not an endorsement of the quality of work. It provides some financial protection for you, the customer. 

Make sure your contractor is properly insured
Ask your contractor for a copy of his proof of liability insurance and bonding or the name and number of his/her insurance agent to call and verify proof of coverage.

Most importantly…Do you trust this person to work on your home?
When it comes down to it, the most important thing to check is your own gut feeling. How do you feel about this contractor working on what is probably your single largest investment – your home? Do you trust this person inside your home? Around your children? Can you communicate well with this person about the project? Are they ‘in tune’ to your needs?