Summit Post details this trail nicely and includes photographs.
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Adapted from Summitpost.org:
This is considered by many to be the standard route up Mount Stuart, it is non technical allowing many scramblers and climbers to have easy access up this peak. Many climbers also use this route for the descent instead of going back down the other various technical routes on Mount Stuart. The climb offers great views of the Teanaway, Enchantments, and some of the other peaks in the Leavenworth area of the Alpine Lakes Wilderness. The route has a few class 3 spots, but has low exposure as long as you stay on route. Throughout most of the year an ice axe is recommended as well as crampons, usually most of the snow is melted out through out July, but sometimes the snow has a way of lingering on snowy years.
Nearest Town: Leavenworth/Plain
Drive I-90 and turn right at exit 85. Turn left onto WA-10/WA-970 which crosses over the bridge over I-90. Then take a right onto Highway 970, (it may also be called highway 10) which goes east for 6.5 miles until you reach a road on your left called “Teanaway Road”, be sure to take this road. As your traveling along you may see views of the Enchantments as well as Mount Stuart, I consider this to be a beautiful drive. After 7.3 miles be sure to stay on the North Fork Teanaway Road (the road changes automatically when passing by the West Fork Teanaway). In 5.8 miles you reach another fork in the road, take a right onto forest road 9737. Stay on this road until you get to the Esmerelda Basin Trailhead.
Leave It Better than You Found It. This should be every user’s goal. Pick up trash left by others, pull noxious weeds along your route, throw branches over unwanted spur trails, etc.
Disclaimer. Treat this information as recommendations, not gospel. Conditions change and those contributing these reports are volunteers–they may make mistakes or not know all the issues affecting a route. You are responsible for yourself, your actions, and your safety. If you won’t accept that responsibility, you are prohibited from using our information.