@Garrett Hollenbach This is an open ended question. There is no limit to the ways and details in setting up a partnership. Its like negotiating a real estate deal, you and your partners own goals/desires plus imagination are your only limitations. That being said, there are a few things I recommend addressing up front, in writing regardless of who the partner is.
1. Exit Strategy - what are you and your partners long term goals? If one wants to sell in 5 years and the other doesnt, that could lead to issues. Play the "what if" drill with scenarios and try to think through and discuss all possibilities. What if the property doubles in price? What is one partner wants out and the other doesn't? What if one partner passes away?
2. Roles/Responsibilities - make sure the roles and responsibilities are clear up front. Is your partner a silent partner only contributing money? If so make sure that is clear and write it down. If something goes wrong and big decisions have to be made, make sure he/she is aware you are the one who will be making that decision.
Once these are cleared up, you can discuss ownership and profit sharing. This can be structured anyway you want, but the traditional way is the money gets 50% and work gets 50%. If you are less experienced, then usually that risk is incentivized by offering up more equity, maybe you get 30%. You can do it any way you want, I would encourage you to find a way for everyone to win, and you will find great success.