See the Getting There section of the main page to get to the trailhead.
From the trailhead, take the trail that heads east for half a mile until it "T"s at the PCT. Turn left and take the PCT 1.9 miles to Gillette Lake. Just before the lake you will cross a paved road (don't worry you can't access it, it's either for the power company or people from the Dam). When you get to a camping area at Gillette Lake, take the right trail at the fork (after every fork or choice you have to make on the trail there are PCT badges on a tree to let you know you chose the right way, you can count on them to help you). You'll cross a stream and then continue on another 3/4 of a mile or so until you pass another small lake. Just after that you will come to a clearing with good views of Table Mountain.
Continue on over a large wooden bridge over Greenleaf Creek. About another half mile and you come to a nice overlook of the Gorge. About another mile on you will come to an intersection of trails. Once again look for the PCT badge and chose the middle trail. The right one is the Two Chiefs Trail and I am not sure what the left one is. You'll soon cross a couple small streams on small wooden bridges and then go through a nice ferny swampy poplar grove before coming to some switchbacks.
Go up the switchbacks and walk along the ridge. Not too far along you'll see Sacajawea and Papoose Rocks to the right. A bit farther and you cross a small stream (might be dry late in the season) and just after that, watch for the unmarked trail to the right. This is the now-closed older trail and there is a large sign indicating such. It's overgrown now and was closed so as to not erode the delicate upper areas of the trail. This is supposedly the steeper on the trails up but, honestly, I didn't see much of a difference between the two. This trail leaves the PCT and climbs through forest for a bit and comes out on the edge of the south ridge of cliffs. It then cuts up through a small boulder field and then a steep meadow to the summit The one thing this trail provided was some neat close views of the cliffs but it really was tearing up the meadows so please avoid this trail.
For the other trail (and now only one) to the summit, continue past this closed trail another half mile to another marked trail on the right. This trail is a bit gentler slope through the forest but then switchbacks up loose rock to the summit. You climb a rocky ridge with great views.
If you have information about this route that doesn't pertain to any of the other sections, please add it here.