The vaccines are essential. Most likely your veterinarian will need you to bring your smartphone and call from your car when you get to the building. If you don't have a smartphone, you will just need to get the attention of the receptionist by waving through the window and making silly faces.
The vet tech will come out of the building to get your puppy, who should be in a carrier if you have one. You may not be allowed in the building if it is not large enough to allow Social Distancing. A vet tech will bring the carrier, with the pup in it, to your car. They would appreciate it if you could pay with a credit card instead of cash.
You should wash your hands as soon as you get home and then wash them again after sanitizing the carrier. If you do not have supplies to do so, you should leave the carrier in your garage or outside for three days. If the pup has a decent recall or if you have a fenced yard, I would err on the side of caution and not take the carrier into your house.
Depending on your circumstances, you might be able to protect your veterinary practice by wearing a mask and gloves when you drop off your pup. Please assume that you are an asymptomatic carrier whenever interacting with the low wage employees we are all depending upon right now.
You will need to reschedule your puppy's appointment for a thorough exam with your veterinarian.
We need to not mess this up. If veterinarians are considered "unessential businesses" then a lot of elderly dogs and dogs with chronic health issues are going to die. To be bluntly honest, so are a lot of people because if my dog started seizing or needed to be humanely euthanized, I don't think I'd really care all that much about infecting random strangers in the heat of the moment.
Some of us seniors and high risk people don't have anybody except our dogs.