Things to look for are quality of care, convenience of location and hours, and cost. That is the summary but so much really goes into each one that those three are not everything alone but more of a "total package". Keep in mind that quality is the most important and good providers are worth their weight in gold (and worth every penny) but it doesn't mean you can afford to pay them that.
Ask questions business type questions such as what the hours of operation are, is there a limit to the hours within the operating hours (such as 9 or 10 hours), when and under what circumstances overtime rates apply, are meals/snacks provided by the center or by the parent, what are the rates, when do they change (age 3 and/or potty trained), and holiday/vacation/personal/sick day closing schedule. Do they have a back up provider? Discuss your needs. Discuss contracts and cancellation terms. What days are they closed? When is payment due?
Ask operational/care type questions such as what their typical days is like, do they have a schedule, adult/child ratios, and what are their discipline policies. Ask to see the play and nap areas.
Ask experience questions...how long has the center been in operation, how long has this provider/teacher been in childcare, what training do they have. Try to get a real feel for the person who will be caring for your child...ask "what if" questions to determine what they would do if a child gets hurt, misbaves, doesn't feel well, etc. Ask security questions like how they handle pick-ups, emergencies, etc.
Ask for references (if they seem uneasy giving info out, ask them to ask a few parents, past and present, and/or others who have knowledge to call you). Ask references what knowledge they have about the center and provider. If they use them now are they happy. If they don't use them why or why not. Ask their honest opinion.
Sometimes, they may give you the "by the book answers" but I always prefered the answers that rang true even if it wasn't exactly by the book. I would recommend going with your gut (even if for no other reason than your mother's intuition you don't like the provider, choose a different one). Also, if you agree to something the least bit different than their contract, make sure it is in the contract before you sign it (and keep a copy).