Red Peak is a big red pile of rocks in the Clark Range, in Yosemite National Park. It is surrounded by beautiful alpine lakes, and is a pretty site from Glacier Point. And it has lovely views from the summit.
First, get yourself to the vicinity of Yosemite National Park, in California, USA.
There are a few main approaches:
1) Drive down the Glacier Point Road in Yosemite National Park. Stop at the Mono Meadows Trailhead. Walk down to Illilouette Creek, and then follow the Merced Pass trail southwards. Now, either:
a) Head off trail in the vicinity of Red Creek and hike up past Grayling Lake to the beautiful alpine bowl between Red Peak and Grey Peak, or
b) Stay on the trail to the junction of the Red Peak Pass trail, and follow the Red Peak Pass trail up toward Lower and Upper Ottoway Lakes.
2) Start out from Happy Isles in Yosemite Valley and follow the Mist Trail or the JMT up to Little Yosemite Valley. Then, leave the JMT and follow the trail past Merced Lake High Sierra Camp and Red Devil Lake, up to Red Peak Pass.
3) Start out in the Sierra National Forest south of Yosemite National Park at the Granite Mountain Trailhead. Follow the trail over Chiquito Pass, past the turn off to Chain Lakes, to Moraine Meadows. Then head over Merced Peak Pass to the junction with the Red Peaks Pass Trail. Now you are on the same path as option 1b above.
No red tape for dayhikes.
If you wish to camp out in the Yosemite Wilderness, or in the National Forest Wilderness, you will need a wilderness permit. If you started at a national park trailhead, you'll need to get a permit from Yosemite National Park. If you started at a National Forest trailhead, you'll need to get a permit from the forest service. Both trailheads mentioned above have a quota. You can either reserve a permit, or walk up and get a first-come first-served permit.
Outside the wilderness boundaries, there are many campgrounds in Yosemite National Park, but they can be difficult to reserve. Plan well in advance, or hope to get a first-come first-served campsite midweek.
There are also many drive-up campgrounds in the National Forest outside Yosemite National Park.
Closer to the peak, in the Yosemite Wilderness, there is good camping at Grayling Lake, Lower Ottoway Lake, and Upper Merced Pass Lake.
Day hike trip reports
Bob Burd's attempt to traverse from Gray Peak
Bob Burd's dayhike.
Multi-day trip reports
Illimitable Illilouette Peregrination
Secor describes the traverse from Red Peak Pass on the south slopes as loose class 2. He describes the climb north west slope from the Red Peak Fork as class 2.
The current page owner followed the Red Peak Pass trail almost up to the pass. He and his partner then climbed up to the base of the first red gendarme, and traversed west until we had passed the gendarmes and could climb up to the ridgeline. We then followed the ridgeline to the peak. Only the approach from the trail to the first red gendarme was loose. The rest of the climb was pretty solid. If we had to do it again, we would climb up the Red Peak Pass trail until we had passed the band of gray rock on the south slopes of the peak. We would have then followed the band of red rock up to the ridgeline. We felt like we followed the Red Peak Pass trail too far.
Bob Burd and various Loma Prieta PCS trip reports describe the hike up from Lake 10,425 in the bowl between Gray Peak and Red Peak, to the saddle above the lake and then on to the summit, as class 2, and decent climbing.
Bob Burd reports that the full traverse along the ridge from Gray Peak is loose class 3 -- too loose for safe travel.