The number one question to ask is if the plumber is licensed. To obtain a license, plumbers must have 2-5 years of experience and pass an exam covering plumbing trades and local codes. That license indicates that they are qualified to solve your problem correctly the first time. Check to see if they have one.
The second most important thing to ask is if they are insured. Only choose a plumber who has liability insurance and workman's compensation. Things can go wrong with any professional trade. And when they do, it's usually at a high expense. Never hire a plumber who does not have insurance. Otherwise, if something goes wrong, you could have to pay to fix it yourself.