F.I. on N reg
Quite simple really. The owner(s) of a N reg a/c can have flight instruction on that a/c provided they get a permit from the Dep. For Transport. In order to get that they need to provide about 6/7 bits of paperwork like ownership details, Airworthiness doc. Registration doc. Maintenance details etc. Takes about two weeks to get.
As for getting paid to do the instruction well of course you need to be a CAA/JAA F.I. and fly from a licensed airfield.