This is not a loop hike so you'll need to leave a car or mountain bikes at the end of the hike to get back to the beginning. The route begins at the Hondoo Arch camping/flat area, at the end of either the McKay flat road or the Reds Canyon road. You can find cattle trails in much of the canyon but for the most part you are picking your own route, choosing where and when to cross the creek. You can't get lost, however, as you simply follow the creek down canyon. The further you go the more time you'll be spending in the water so it's best to just put your wading shoes on from the beginning and enjoy the water.
In about 4 to 5 hours you'll reach a very deep section of the creek -- some
guidebooks don't mention this pool, which makes it seem likely its creation was a fairly recent occurrence. During spring runoff the water in this pool can be up to neck deep (or higher!) in it's deepest parts and chest deep through the rest. By mid-summer the water here should be much lower. This section is about 50 feet long and is unavoidable. Adventurous hikers will find this one one of the highlights of the trip. Except for this one deep pool, Muddy Creek at it's deepest should only be thigh-high in spring runoff and calf-high in the summer.
In 20 more minutes you'll reach the log jam. About half an hour past the log jam the canyon begins to widen, signaling the end of the Chute. About an hour more and you'll reach the entrance to Chimney Canyon, easily identified by two huge boulders on opposite sides of Muddy Creek.
An hour from Chimney Canyon, keep an eye out for a rough but well-defined road going up a cliff on your left. Go up the road to the Hidden Splendor Mine where you've hopefully left a vehicle or bikes. Drive or bike back to Hondoo Arch (16 miles, with a 1700 foot gain the first 7 miles).
Hiking time varies drastically depending on the amount of water in the creek, the fitness of the hikers, lunch breaks, Kodak moments, and the weight of your packs. All times listed above are assuming you're in relatively good shape, carrying only day packs, and keeping a steady pace. If this is the case plan on about 6 to 7 hours hiking time (not counting breaks) from Hondoo Arch to the Hidden Splendor Mine. If you're doing this as a one-day hike from Salt Lake City you should drive as close as you can the night before to the hike's beginning and car camp (otherwise you're looking at one VERY long tiring day).
Backpacking: In high water with heavy multi-day packs and/or a liesurely pace you'll need to watch the time closely and count on up to 11 hours for the whole hike. There are no places to camp in the Chute safely. In other words, you'll probably end up camping at the end of the Chute (~8 hours) or by Chimney Canyon (~9.5 hours). In low-water season backpacking time will be much faster.