You'll want to read this in conjuction with a suitable map, such as a DeLorme atlas, topozone.com, or the like. The description starts at the north end of the trail.
The whole trip is about 100 miles, so hiking it without resupply is an option (say, 6 days of 15 miles each). But there's some information about resupply points, and dealing with a dog there, in the following description.
|start||The Rush Creek Trailhead is located on the June Lake loop (highway 158), across the road from Silver Lake. There is a small booth which can issue wilderness permits during limited hours; otherwise you'll need to get your permit elsewhere (Mammoth Lakes ranger station, I think). Stores and other facilities are available along the June Lake loop south of Silver Lake, or in Lee Vining or Mammoth Lakes.||8.8 miles||Follow the Rush Creek Trail past Agnew Lake, Gem Lake, and Waugh Lake. These hydroelectric lakes were allowed to remain in a wilderness area due to special provision of the Wilderness Act. The trail crosses the tramways that haul up equipment for the dams. A mile or two after Waugh Lake, you'll intersect the John Muir Trail.||6.4 miles round-trip (optional)||If you want to hike all of the dog-allowed parts of the John Muir Trail, you can hike up to Donahue Pass and back (dogs are not allowed north of the crest of the pass).|
|70.0 miles||John Muir Trail, from Rush Creek Trail to Piute Canyon. Consult one of the many guidebooks for the John Muir. Your first resupply chance is Reds Meadow, 17.5 miles from the Rush Creek Trail junction. The Reds Meadow store is small but not out of the question for resupply, or you can catch the shuttle bus to Mammoth Lakes (dogs are allowed on the shuttle bus). I don't remember any outdoor seating at the The Reds Meadow cafe, so it might be a bit tricky getting a meal with your dog here. Your second resupply chance is Vermillion Valley Resort, which is near the Mono Creek Bridge, 29.2 miles from Reds Meadow (from the bridge to the resort is either about one mile of hiking plus a ferry ride, or about 7 miles of hiking if you don't take the ferry). They welcome hikers and well behaved dogs (their web site has a page on what they expect from canine visitors). The restaurant has plenty of outdoor seating, or indoor seating with good views outdoors, so it is easy to dine with a dog here. Don't count on the store for much in the way of resupply - you might (or might not) be able to buy dry dog food by asking but you won't just find it on a shelf. The only other resupply chance on the trail is Muir Trail Ranch, but what they can offer the through-hiker is more limited (and expensive). They don't in general welcome dogs (citing concerns with how your dog gets along with theirs). Perhaps a dog would be OK if you are just picking up a package, but I'd ask first.|
|10? miles||Up Piute Canyon to Piute pass|
|about 5.5 miles||from Piute pass to North Lake trailhead. The North Lake trailhead is said to be well marked.|
My dog and I have only test-hiked the stretch from Reds Meadow to Mono Creek Bridge (Vermillion Valley Resort), and from the Rush Creek Trailhead to Gem Lake. But from browsing the web, all of these seem to be relatively well-travelled trails.
John Muir page from Russell Bell, including trail mileages.
Canine John Muir