What is the process of buying out of a mortgage?

My sister and I own a home. Both of our names are on the mortgage and originally needed both our credit to be approved for this size mortgage. We are now looking to either sell or buy one of the other out. We know we will take a loss if we sell now but don’t know if either of us can afford to own it on our own. What do we need to do to buy one out? I heard we have to refinance, one will have to get approved for the amount of the mortgage on our own, and repay closing costs? Is this true? Are there more affordable options? What is the process?

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