There are a few places you can start this adventure, but starting from the South Climb Trailhead and Cold Spring Campground is a good option. It mostly means that you are going through the Yakama Reservation, where there is no trail early in the run, but you'll also cross the major water crossings before they swell too much.
From the trailhead you'll gradually climb up to the Round the Mountain Trail for about a mile. There is a campground called Timberline at the junction, and this is a good option if your first day is a short afternoon to camp, but the warm up to the trail is worth it because the hard stuff is ahead.
Turn right at the junction and follow the rolling Round the Mountain Trail in and out of the forest, crossing a few creeks along the way. The next junction is the Snipes Mountain Trail off to the right. Keep going, the views are coming.
Going forward, the trail rolls and reaches the Bird Creek Meadows area. July and August would be prime time for wildflowers here. Not far beyond the Meadow there will be a trail off to the left called Trail of the Flowers. Even though there is a choice to stay on the Round the Mountain Trail, go left onto the Trail of the Flowers as the Round the Mountain Trail doe not actually go around the mountain. Follow this Trail of the Flowers for about a mile and you'll reach the first ridiculous view of Pahto at Hellroaring Viewpoint. Get ready for the real adventure to start.
A GPS device or a map and compass are important at this point. The trail disappears for about 9 or 10 miles through some of the roughest terrain on the mountain. There are two lines to take: The higher one requires snow tools like spikes or crampons and an axe most of the year; the low line leads through thick brush, down scree slopes that descend over hundreds of feet in short order, across raging creeks swollen with runoff, and over rocks and boulders. And once you do all that, all of a sudden you will be back on the trail and on your way. It will be slow going through this area, but savor all the amazing views, take your time, and make sure you are on course.
Once back on trail, the going gets way easier and more wide open, which is a great respite from what just transpired. The trail that just appears is called Highline Trail, and this is the one that takes you to the the Pacific Crest Trail. Follow the Pacific Crest Trail for a while with some great views until you meet up with the Round the Mountain Trail, and you are home free!
Note: Before you go on this trek, give the Yakama Nation a call and talk to a Ranger to make sure the trail is open to backpackers or hikers: 509.865.5121 or 509.395.3402