There are a few different ways to organize this, but mostly I think you need to talk to a lawyer. The 50/50 split thing should be in writing along with a bunch of other issues.
You could have one of you doing a sole proprietorship where the other person is a contractor that receives half of all revenues/profits. The person that owns the sole proprietorship may be entitled to deduct certain costs of running the entity. The other person would then be 1099'd his share of revenues.
You could set up a partnership, again legal paperwork is necessary.
You could also setup an S-Corp, where each of you is a 50% owner.
You could also setup an LLC that is organized as any of the above. I would only do this if you can self fund some additional tax preparation costs. Figure about $600/year at a minimum.
There are a lot of options with a sole proprietorship being the easiest. Your first step on the new venture would be to apply for an EIN (free), and then opening a business bank account.