I don't have kids, but my mom works for a family 2-3 days/week babysitting for them (the Mom works full time days and the dad works 12 hr days). She replied to their newspaper ad, and the Mom asked her to come for an interview to meet the kids and talk with them. She's been babysitting in their home for about 3yrs now.
If I was looking for a permanent sort of daycare (like if I'm working part or full time and need somewhere to leave my kid(s) ), I'd want to go see the centre/home alone or with my spouse and talk to the provider. I'd especially like to go when other children were there to see how the place is run.
Depending on how I felt on the initial visit, I'd probably ask for references, and maybe even talk to the kids who are cared for there ('So, do you have fun when you come to Daisy's?'). I'd also demand a clean CPIC and that the daycare provider had current First-Aid/CPR certification and a Fire Escape Plan (hey, I'm a FF, I automatically check for smoke alarms everywhere I go!).
Then I'd like to take my child to meet the person before leaving them there.