You can resign at any point, as long as the game is still ongoing. You can resign during your opponent's move, for instance. In fact I'd say it's unusual to make a move before resigning -- most people resign because they don't see a good move anymore.
If it's already ended some other way, you can't resign any more. Some people don't want to win on time in a clearly lost position, for instance, but then they should resign before a flag fall is noticed. And if you resigned but later find out that you actually checkmated your opponent earlier in the game (but didn't notice at the time), then you actually won because checkmate ends the game immediately. Yes that happens, mostly in youth tournaments. (Edit: that's FIDE rules. This sort of thing may well be different under USCF rules, I don't know).
There is nothing about the exact procedure in the rules, probably because resigning ends the game and usually makes the opponent happy regardless, so there's never been a need to regulate it. A good way is to stop the clock, say you resign, and shake hands. Write down the result on your score sheet. The important thing is to make sure that the opponent understands your intention.
Official tournaments usually need a signature somewhere (on the score sheet, or on separate little result forms). Make sure the result is recorded correctly on it, that both players sign, and that the arbiter gets the signed form.