There is no right or wrong answer, @Andy Acosta. Traditionally, when someone is paying all the costs, i.e. purchase and rehab, and you are doing all the labor (acq., rehab, selling, etc.) then you would split the profit 50/50 as a partnership.
Your friend would buy the property outright using an entity he controls 100%, and there would be a partnership agreement between you and that entity. Don’t forget, he’s taking all
the financial risk. If you are not able to perform, per your partnership agreement, he could “fire” you and perhaps pay you a finder fee of some sort (or nothing since you’d likely be leaving him with a mess).
If the deal goes as planned, you would evenly split any profit from the sale after all of his costs were subtracted.
On the other hand, your friend could fund the purchase and even rehab costs to you as a private loan, using professionally prepared loan documents. You would do all the work. In this case, you would own the property 100% but with a first position lien from your friend.
You could make monthly payments to him or pay everything to him when you sell, as negotiated into your loan docs. Here, he would be entitled to his interest (and points if he’s sophisticated enough to require them) and you would keep the remaining profits.
Only about 1347 variations on this, but those are the basics of an equity interest and a debt interest in a flip. (I'm assuming a flip since you weren't clear.)
Just so you know, it typically works out that hard money lenders will end up with about 25% to 33% of the profit in a flip, for relatively little risk. In a 50/50 partnership, your partner will obviously get 50% but incurs all the risk. That is, even at the confiscatory rates most HML's charge, financially you're almost always better off borrowing the money.