It's a very good idea to figure out who your vet will be prior to bringing home your kitten. Not only will you want to schedule a checkup to make sure your kitten is doing well and to discuss vaccination and checkup schedules, but it is good to have a relationship with a veterinarian should you have an emergency and need immediate care. It is a lot easier to be seen by a vet who knows you and has your kitten's medical records than calling around to try and find someone willing to see a new patient in an emergency situation.

We've found our recent vet by asking another vet. In the past we've found vets by speaking to other pet owners. You may also want to try and post on any online community groups or social media sites asking for recommendations.

Here's an article from the American Veterinary Medical Association on finding a new vet.

Once you've found a vet, ask them for recommendation for an urgent care veterinarian. This way you have the information should you have an emergency outside of your vet's office hours.