From the Denny Creek trailhead, walk north following the Mt. Yale/Hartenstein Lake trail on the west side of Denny Ck. It initially switchbacks steeply up the mountainside for the first half mile, following an old, rocky roadbed. After about one mile and/or 30 minutes of hiking, you'll come to the Mt. Yale turnoff. This is at least a quarter mile or more after crossing Denny Creek to the north/east side and is an easy to identify intersection.
Once on the Mt. Yale trail, follow it NE to where it crosses Delaney Creek and then begins a steep ascent up the open west side of Yale's SW shoulder. Follow the well-established trail to where things flatten out on the ridge at 12,200 ft. Continue north on the trail and ascend to about 12,600 - 12,800 feet. Depart the trail here and begin a long contour east toward the saddle between Mt. Yale and Mascot Peak. On this traverse across the south face of Yale, you'll cross several gullies, some of which will require a little extra attention to find a way across. Overall, the terrain will be a mix of tundra and broken rock of various types & sizes. Expect some boulder talus at times that will slow progress & require some rock-hopping. Don't be surprised if you flush out a group of Bighorn sheep that like to hang around here, away from the 14er-bagging hordes.
At the saddle, turn south and simply follow the sometimes rocky ridge to the summit, about another 20 minutes away. We did this climb on a late August, full moon night and arrived at the saddle right at sunrise and the summit shortly after. With a 3:00 AM start, it was easy to follow the Mt. Yale trail in the moonlight. By the time we were making the traverse across the south face of Yale, there was enough morning light to see what we were doing without breaking a leg.
For the return hike, simply retrace your route back to the Mt. Yale trail and follow it back to the Denny Creek TH, offering a friendly greeting to the numerous 14er-baggers you'll see along the way. Or, for extra credit, join the 14er crowd by hiking north from Mascot peak to the summit of Mt. Yale on the Yale south ridge. Much of that ridge is somewhat arduous with a mix of tundra and large boulders along the way and increasing rock as you approach the summit. Then, follow the Mt. Yale trail all the way down.