The South Ridge is the only described route that I am aware of. The north ridge looks a little more difficult to access. Approaches from Wildhorse Basin would likely involve very steep climbing.
after reaching the Kane Lake Trailhead (7600ft), your first goal is to take the trail to Kane Lake. This trail is fairly well maintained for 2 or 3 miles. The last mile to the lake crosses some talus and rock slabs before climbing up a glacial shelf- you will need to keep your eyes out for cairns. It is about 4 miles to Kane Lake (9300ft). There are good views of Devil's Bedstead West as you hike up the valley.
From Kane Lake, the goal is to head south and east to reach the saddle south of Abel Peak. The terrain above the lake will almost force you to go in the correct direction. Hike up combinations of tundra, talus and rock slabs to get into the upper basin and at this point Abel Peak will be visible ahead. To your right, Goat Peak looms overhead. After crossing some big talus, reach the saddle and peek over into Wildhorse Basin. Turn left and head up the south ridge. It is probably easiest to climb a little west of the ridge crest. It is mainly class 2 with a couple of class 3 moves depending on your exact route. There is a bit of exposure at times into Wildhorse Basin. The view from the top is superb.
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"How do you distinguish between being off-route and putting up a first ascent?"