This route description begins with a climb of Taylor Peak. See the route description for that peak first. The description for Star begins from the summit of Taylor. One-way mileage and elevation gain are measured from the summit of Taylor.
From the summit of Taylor Peak, hike SSW along the ridge crest to about the 12,800 foot contour. Make a decision here. Option #1: You can continue on down the ridge, negotiating a steep, rocky section, to the first saddle and then climb up over 200 feet in elevation as you continue following the ridge to a minor high point. From that high point, descend again, losing about 300 feet to the next saddle. Next, re-climb another 300 feet to continue along the ridge. This time, you'll regain about 550 feet. After you pass the 13,135 marker, the ridge turns into a jumbled mass of rocky spires and outcrops, followed by a deep gash. (Good luck here. We have no idea how easy or difficult this section is.) Keep following the ridge until it turns south toward the Star summit, losing yet another 200 feet in elevation before gaining the final 400 to the summit.
Option #2: If you don't like option #1 with all the ups and downs and rock obstacles along the way, then here's a better alternative. Back at the suggested point of decision, descend south off the ridge for 400 feet elevation on a tundra swath, then turn SW and contour around a minor ridge and below cliffs into a large basin east of the Star summit, that's mostly a rock glacier. Overall, you'll lose about 600 feet from the point of decision. Hike and scramble your way across the boulder field aiming for the saddle north of the Star summit. From the saddle, turn south and hike and scramble over lichen-covered boulders and rocks to the summit. When we climbed this summit, it was raining much of that day and the lichen-covered rocks were banana-peel slick. Though crossing the rock glacier and following it up to the saddle is tedious and not much fun, this is still a better alternative than trying to follow the ridge all the way over from Taylor, in our humble opinion.
For Star alone, we would suggest hiking SW on trail #582 until just before it begins to climb up south above the Taylor River. Leave the trail, cross the river and hike on the west side of the drainage that comes down from the large basin east of Star. Once on the rock glacier, follow the hiking directions in Option #2 above.
For a return route, descend north back along the north ridge of Star, descend east back into the rock glacier and then SE to exit the basin and get onto some tundra. Stay on the west side of the developing drainage and hike down through increasing trees all the way back down to the Taylor River. Cross the "river" (mostly a nice creek here) and pick up the forest trail # 582 that will lead back to the end of the road and your parked vehicle. You can also try picking up the FR761.1D after you exit the rock glacier basin and follow that road back as it contours between 11,800 and 11,600 feet to where you first intersected it as you headed up from the parking area to climb Taylor.
Links to other information, routes & trip reports for this peak that may be helpful.