Start with the agreement you already have
Many LLC operating agreements, partnership agreements and shareholder agreements contain buy-sell provisions. They may say what triggers a buy-out, how the price is set, for example by formula, by appraisal or by agreement, and how payment is made, such as installments over several years. Read them first, ideally with your attorney, because they may decide much of the process for you.
If there is no agreement, or it is silent on the issue, the owners negotiate, and a neutral valuation often becomes the anchor. Either way, both sides need access to the same information at the same time.