You need a purchase contract with your parents at a price that will cover their costs plus their remaining mortgage amount. You don't need a realtor so a realtor commission is not factored in. But they will have a share of the title costs, title policy, etc. Talk to a title company for a list of normal fees and who pays what. In different states customary charges to buyers and sellers are different. For example, in Texas it's customary for the seller to pay for most of the new title policy.
With an agreement in hand you can apply for a mortgage. Call a broker and call a bank and discuss what you want to do and they can explain your options. Pick the one whose service level and terms are more satisfactory to you.
Once the new loan is closed the house will be recorded legally in your name and your parents will be free of their current mortgage obligation on that house. As a bonus, your credit will be improved by having a mortgage in your mix of credit trade lines.
This transaction can be done all the way down to a 640 credit score by going with an FHA loan. Some lenders will even allow 620. There are also ways to include some of your costs in the loan since the home will obviously appraise for more than you are buying it for. You could do that transaction for the 3.5% down payment only out-of-pocket if you wanted. This is the part you need to decide with a mortgage loan officer, whether it's with a bank or a broker.
I'm a mortgage broker licensed in Texas only.