Does the shop appear to be clean and well maintained? A shop that does not appear to be well kept might also be a shop that puts sterilization (your health) at the bottom of their list.
Check for the following:
Current business license for tattooing & piercing by the city and state?
Does each tattoo artist have a license to tattoo or pierce?
Do the artist have CPR/AED and bloodborne pathogen training as required by law?
Does the shop explain the sterilization process in a manner that is reassuring to you? Not just try to blow past the question with a smile or humor.
Does the shop allow you to view the sterilization room upon request?
Does the shop make their annual health inspection reports available for public viewing?