This may be the quickest way up the mountain. Certainly this way is not as steep as the Northwest Route.
The shortest approach for this climb is from the Mirror Lake Trail, which starts from a few miles up FR-5480 (which junctions off of FR-54, the Stampede Pass Highway). The trail starts at approximately 3,750 ft. It is well-used. In about 1/3rd of a mile diminutive Cottonwood Lake is reached, and in one mile the northeast shores of Mirror Lake are reached. The junction with the Pacific Crest Trail is here. The east side of Tinkham Peak can be seen rising above the lake. Follow the PCT south along the lake to its outlet. Cross the outlet and locate the flagged route by gaining the toe of the Southeast Ridge south of the lake.
I did not pick up the trail at the outlet but found it shortly thereafter. Pass a camp and look for flagging. The route is over-flagged (every 30 feet!), in my opinion, making it very easy to see where you need to be going. If you lose the trail, simply keep to the ridge crest or slightly south of it and you'll soon relocate the trail. The flagging eases off higher up but by this time the route (and trail) are obvious. The trail stays to the north side of the constant signage saying "Cedar River Watershed--Source of Seattle's water supply. Trespassers will be prosecuted."
Eventually, the trail will break out in the final alpine summit slope whereupon it more or less becomes indistinct. Simply ascend the slope about 50 feet left of the east-facing cliff to the East Summit. This is the summit that has been triangulated at 5,395 ft. From the East Summit it may appear that the West Summit is higher. The exposure on the north side of the mountain is quite intense, so be careful.
There is a good boot path between the East and West summits. It will take about 10 minutes to make the transit. Two hours from car to summit, approximately. There is a register at the West Summit.
One can descend the Northwest Route back to the PCT to make this a loop trip (recommended) or go back the way you came. The extra time needed to make it a loop trip is inconsequential (maybe 20 minutes).
The gear you need is dependent on the season and conditions. The route is non-technical, though an ice-axe might be handy in winter.