From the Forest Service, gated trailhead, walk south along the old roadbed. The Three Apostles will loom over the southern horizon and you'll be able to clearly see them. At about 1.25 miles, the main trail begins to turn SE and is a well-used descent route for hikers coming off Huron. Where the USGS map shows the old townsite of "Hamilton," and the trail turns off for Lake Ann, go about another 1,000 ft. and watch for a trail that breaks off the main and continues south crossing an eastern fork of South Clear Creek that drains the south side of Huron, and then crossing the main south fork of Clear Creek. This is how the Trails Illustrated map shows it and how G&M described. If the trail has been re-routed, try the Roach description. Roach has you turning off onto the Lake Ann Trail, (which serves as both the Colorado & Continental Divide Trail at this point), then crossing to the west side of the south fork of Clear Creek, and then turning south to join the Three Apostle's Trail. This trail that breaks off is well-used and continues south through forest gaining elevation along a ridge on the west side of that south fork of South Clear Creek which at times is below and very well entrenched. The trail delivers you to a flat meadow area with abundant wildflowers at 11,360. There are some good camping spots in this area if backpacking in. The best are scattered among the stands of evergreens at the north end of the meadow. West Apostle will be directly south. You should be standing near the foot of a vast rock glacier that comes down from the steep couloirs of Ice Mountain and West Apostle. This meadow is where climbers will break off to the SE for North Apostle and Ice Mountain. A use trail will lead to the basin between North Apostle and Ice Mtn.
From this point, Roach has you gain a small tarn at 12,100 ft, skirting a cliff in the process, and providing no other detail. When we climbed this in 1994, the trail we had been on became vague and wandered through the meadow crossing the stream a couple times before committing itself to the eastern slope of the basin. We followed it through willows and boulders at the foot of the rock glacier, then went up a steep western flank of N. Apostle. At this point it was still mostly all tundra. The dramatic NW ridge of N. Apostle terminates above this basin area. To gain access to the upper basin between N. Apostle and Ice Mtn., we headed in a direction that took us first on the west end of that NW ridge, then to the south side of the base of that NW ridge along a steep tundra slope. After gaining about 600 feet elevation, we turned more to the right to cut across a rocky and cliff-filled slope to get into the upper basin. By now, we suppose there is probably a well-established, cairned route, but at the time, we followed a nice tundra-covered bench through the minor cliffs to reach the center basin. G&M recommended a higher bench which would probably have worked just as well. The one we followed looked more inviting - less rock & more tundra. At the far south end of the bench, we began hiking more in a SE direction to gain more elevation. All of this brought us to/slightly above the small tarn that Roach mentions at 12,100 ft. It's difficult to represent this on the map provided. Getting to here will be the most complicated part of this climb.
From the small lake/tarn, the basin stretches out to the SE. It's never really visible from anywhere below. The remainder of the hike is fairly straightforward. In earlier season, expect this upper basin to be largely snow-filled. If later season, expect plenty of rubble. To get around the lake/tarn, we climbed above it on the north side crossing on rock slabs and then heading across a boulder field before contouring back into the center of the basin. A tundra slope leads up for about the next 600 feet to about the 12,800 foot level. After that you'll have to resort to crossing large boulders and rock-hopping. When we climbed to here in 1994, the remainder of the route to the Ice Mountain - N. Apostle saddle was on snow. Ice axes were useful. If there's no snow here, it will be a lot of loose, rocky rubble. Breathe a sigh of relief when you finally reach the saddle, but don't relax yet. It's more of the same for the entire SW ridge of N. Apostle all the way to the summit. In 1994, there was faint trail & cairns marking the way. The cairns were pretty much useless. The final 500 feet, though a little tedious, is never too difficult and follows a course of small, sandy gullies where possible weaving among the rocks.
The summit of N. Apostle offers a chance to look down on the impressive west east and north faces/ridges of the peak. These are far more challenging. The summit also offers a chance to study the route up to Ice Mountain via the connecting ridge. If continuing on to Ice, spending a little time here will prove valuable in navigating the challenges on the upper part of the ridge. There's an impressive view of Huron to the north and to the south, Waterloo Gulch, which has a trail, offers some intriguing backpacking options.
Links to other information, routes & trip reports for this peak that may be helpful.