Dana's answer is very good. I'll only add a little bit of detail.
Many companies stay as General Partnerships until there's some reason to protect the founders' assets, sell shares, fool with taxes, or otherwise get the benefits of incorporating. You can continue as a GP as long as you like.
You don't mention whether or not your associate is a US Citizen. If not, it may be difficult to incorporate in the US. Even if your associate is, be conscious that many states have limits on what share of a company a foreign citizen can own. You may want to shop beyond just the obvious DE and NZ incorporations and look for a state that is friendly to your particular international interests.
Business registrations depend on just where you're doing business from. Usually there's some city license, possibly some county license (most cities are in counties), and usually some state registration (cities and counties are in states). These days, cities, counties, and states have actually gotten pretty good at being user-friendly and telling you what to do to get in compliance. (Years ago, it was your job to figure it out, but they'd still go after you if you didn't... turns out they make more$ this way!) Call yours or go to their Web site. There'll be some fixed price but it's usually pretty low. You can get fined if you operate without these licenses in some jurisdictions.
Compared to your overall startup costs these costs should be pretty low, even if your other costs are just "buy that new laptop I deserve."