The transaction is really a hybrid refinance/purchase. I would start by applying for a loan to purchase the 50% of the property that you donâ€™t already own. A good lender can go over your financial situation and advise you as to what loan will work best for you and your situation. The lender will do an appraisal and you can then base your value and how you want to share the costs after you have that information.
There is a lot more to this type of transaction that I could ever write here, but I would be glad to go into more detail if you want. You can contact me through my profile.
First contact your local real estate agency or get the name of a reputable agent. Interview several agents and the one that will give you free information and advice go with him/her. This agent should be able to provide comps for similar homes being sold in your are. Once you have an ide of what your home is worth. You may offer to buy your sister's share and transfer the title in your name. You will need a lawyer to process this and execute it.
If it will be an investment property and you have tenants in, you can get an investment mortgage to pay off your sister.