We recently published this article about the re-opening of Jersey.
From Monday, you are free to visit Jersey and stay in a hotel. As long as you live in a Green-listed local authority, you can take a free PCR test on arrival and then remain in your hotel for 6-12 hours until the result comes through. After that, you are free to do what you want.
There is no testing or quarantine of any sort on your return to the UK as Jersey is in the Common Travel Area.
My article with all of the information on visiting Jersey is here. The newly published list of which UK local authority residents are allowed to enter is here.
IMPORTANT: Heathrow Airport and its surrounding area is on the Amber list as it is part of Hillingdon. Do NOT spend the night at the airport or in any hotel in Hillingdon before your flight as you will be forced to spend five days in isolation on arrival.