How do I determine a price for buying out an equal partner?

This is mostly a matter of negotiation. There are no firm guidelines. You can get some idea, if you're lucky (and are in a relatively common type of business) by looking at some of the links produced by a google search for "valuation guidelines". The idea is a lot like valuing houses, looking at comparable transactions, then adjusting for growth rates, location, history and other factors that matter. Usually the guidelines have to do with multiples of sales, profits, book value, resale value of assets or a few other formulas. Nothing is written in stone.

Unfortunately nobody's business is standard, so that gets hard. If you have a lawyer you both trust, he or she might be able to help. Mediation isn't uncommon.

Good luck with this,
Tim