I,ve done myself and the process is rathet more complicated than the previous replies suggest. I'm a Brit in the USA. I came here 4 years ago with CAA CPL/IR and instructor rating. The only thing "given" to me by the FAA was a limited-use commercial certificate (no use for earning money!). I had to go through the FAA mill:
written and flight tests for the commercial certificate, instrument rating and FI certificate. But, it was worth it! I had
a terrific time instructing in California.