When the wort is fully boiled and ready to cool, transfer the pot to the sink from the stove and drop in the coil. connect to the faucet and turn on the cold full blast. Cover the brew pot and let the water run into the sink until tepid or room temp. Remove coil, pitch yer yeast in and put it in the brew pail. Stir in a little air with a drill and a stainless of plastic rod with right angle bend in the end.
Follow the usual instructions. Rack on time. Bottle whenever. Add dextrose priming sugar (I lean on it a little for extra carbonation). Bottle and store for a good long while - I find a couple months to be best.
Prosit, comrade!
You should coil most of it around a 3# coffee can to increase the cooling path and surface in the kettle. All but about the last 3 feet on each end (depending on the depth of your brew kettle. Should have about a 1’ overhang on each end to keep drips out of the kettle.
And you can eliminate some of the sanitizing hassle by putting the coil (without water hoses being connected) into the brew kettle for the last 15 minutes or so. Might as well let all that nice boiling hot liquid do the work for you...
Quick-connect garden hose fittings and garden hose work well to bring the water to that very hot pot full of boiling stuff. And to take the warm water to wherever you need it.
“relax, don’t worry, have a homebrew”