First, welcome to the forum. When you get a moment, stop by the intro thread and say hello.
You have two sets of laws to deal with- State and Federal. There are several states that do not permit private ownership of machine guns. The other law (as mentioned) is the 1934 National Firearms Act.
In a nutshell, you must be 21, not prohibited from owning an ordinary firearm, and have a REAL healthy checkbook. A LEGAL, TRANSFERABLE M16 rifle is selling for between $15,000 and $16,000.
You will need to find a Machine Gun Dealer in your home state, since the transfer MUST pass through such a dealer- they can help guide you in the process. It includes being fingerprinted, supplying passport photos, approval from local Chief LEO, application, paying a $200 transfer tax, and waiting about 6 months.
As mentioned, ONLY the full auto firearms that have ALREADY been registered with the BATFE by May 1986 CAN be legally transferred to a private citizen (which is why the price is so high- finite supply of them)