How does a non US pilot buy a N reg plane?
The ownership requirements for registering an N-reg aircraft are discussed in this question. The current FAA information says that the only options open to a non-resident foreigner are:


  
  A corporation or association:
  
  
  organized under the laws of the U.S. or a State, the District of Columbia, or a U.S. territory or possession,
  of which the president and at least two-thirds of the board of directors and other managing officers are U.S citizens, and
  in which at least 75% of the voting interest is owned or controlled by persons that are U.S. citizens,
  
  A non-U.S. citizen corporation organized and doing business under the laws of the U.S. or one of the States as long as the aircraft is
  based and primarily used in the U.S. (60% of all flight hours must be 
  from flights starting and ending within the U.S.)
  


So you either need a corporation that's majority controlled by US citizens, in which case there are no restrictions on flight activities; or, you can use a non-US citizen corporation but then most of the flight hours have to be in (or to/from) the US.

The ideal way to go about this would be to find someone near you who's already done it. Many flight schools and individuals outside the US operate N-registered aircraft so you might be able to find someone who can tell you how they did it. You'll need to do this research anyway, because if you're basing an N-reg aircraft outside the US then you'll need to find an FAA mechanic near you who can legally perform maintenance on it. If your country has some kind of GA or pilot's association then you could ask them too.

You can also look for companies (usually law firms) who specialize in doing this and get their advice and/or retain them to actually set up the ownership structure that you need. That's going to cost some money - and many firms are focused on business jets, not light singles - but it could be a minor cost compared to the aircraft and maintenance, depending on what you plan to buy. I found a few by Googling but a personal reference from someone near you would be a lot more useful.