Just purchased a medical practice to add to my current practice, no inventory. Making monthly payments to previous owners. How do I book this in Quickbooks desktop?

The purchase if both equity (for the practice) and a liability (for the amount you owe).

To set up the purchase, create one of each of these types of accounts and then record one transaction in the equity account for the amount you agreed to pay for the practice using the liability account as the other account.

Then when you make payments, use the liability account, which will pay it down.