There's a reason why this slot is not well visited
Greenehaven Canyon is a narrow, short canyon that starts just south of the Arizona border and ends at Lake Powell.
This is a slot canyon - flash floods can be dangerous. Do not enter this canyon if rain is forecast. If you are in the canyon and you hear a flood coming, escape up the canyon walls if possible. Know your escape routes. Page Sandstone is not very cohesive and is very difficult to gain purchase on - climbing up and down slopes that would not be a problem with other dune-laid sandstones (slickrock) are difficult to impossible in the Page.
The hike starts just off of US89, south of Greenehaven. Duck through the barb-wire and proceed to the wash bottom. The wash is broad and sandy at the beginning. Follow the wash as it narrows. There is a minor pourover that can be bypassed on the left about 100 yards from the fence. Take the old cow trail that starts at the pourover. It drops you back down to the canyon bottom, where you continue. The wash bottom is sandy, a preview of the rest of the hike.
About a quarter mile downstream from the pourover there is another. This second pouroff can be negotiated with ropes, but it can also be bypassed on the right. Follow the cow trails along the rim and up to the ridge top. This will lead to a Page Sandstone ridge which drops to the confluence of Greenehaven Canyon and a tributary entering from the east. You can scramble down this ridge easily and follow the canyon downstream towards Lake Powell or turn left and go upstream. This description is for the upper portion of the canyon, between the large pourover and the fun that can be descended at the side canyon.
Once down the fin, backtrack up the canyon to the pourover. The canyon is not terribly impressive. The Page Sandstone is very crumbly, so there are constant rockfalls to dodge. The walls are never more than 50 feet high in the backtracking section. The upper part of the canyon, between the pourover and the ridge, is also terribly frustrating due to the amount of burrs you'll end up with in your socks. I had to stop about every minute to pick new ones out, ruining a new pair of socks. Gaiters are practically required.
Once you have exhausted your patience, turn back, climb the fin, and make your way back to 89.
None, save for the lake if you go that far.
The hike is within Glen Canyon National Recreation Area, which allows "at-large" camping, but few good spots present themselves. You would also be very close to peoples' houses. Go the two miles down the road to Lone Rock if you want to camp nearby.
Check out the Official Route and Triplog.
WARNING! Hiking and outdoor related sports can be dangerous. Be responsible and prepare for the trip. Study the area you are entering and plan accordingly. Dress for the current and unexpected weather changes. Take plenty of water. Never go alone. Make an itinerary with your plan(s), route(s), destination(s) and expected return time. Give your itinerary to trusted family and/or friends.