If parked in the upper parking lot at Andrews Lake, hike down to the lake and find the trailhead at the NW corner of the lake near some vault toilets. The trail starts out paved as it goes around the west end of the lake and turns to gravel after crossing the lake outlet. This is trail #623. Once on the south side of the lake, it begins climbing uphill through forest on a series of gentle switchbacks, gaining about 400 feet in elevation. This is a well used trail. Continue up 5 switchbacks and then start keeping watch for the trail that cuts off for Snowdon Peak. The turnoff was marked by a large cairn. These coordinates should be close to that turnoff: N37° 43' 15.82" W107° 42' 26.31". You can see this turnoff on Google Earth. This trail to Snowdon will take you past some small tarns, crossing a couple of very minor ridges and to a large, grassy meadow where the trail may fade some. Re-enter a stretch of forest at N37° 43' 10.95" W107° 42' 01.90" and hike to another smaller meadow and on the left side of that meadow, begin the real ascending for the day.
Follow a large, grassy couloir up to a saddle north of Snowdon Peak and south of UN 12,628. This involves about 1,000 feet of gain. It's never particularly difficult. At the saddle, turn southward and follow the ridge SW to another saddle. The trail stays to the left side of the ridge across ledges. As the ridge levels, slabs of rock appear. Continue following a cairn-marked trail that will lead off the main ridge and onto the east side of the mountain. This is to avoid some more difficult obstacles farther up the ridge. Contour across the east face some, losing perhaps a little elevation and then contour a little more. Begin heading up with some serious ascending, at times on some very steep terrain of combined rock and tundra that requires some 3rd class scrambling. At this point, it's easy to get off any designated route and you may miss the intended access, but continue working upward. At one point, we followed a rubble-filled gully that had beautiful clumps of columbine. Either work back to the NE ridge either just below the summit or emerge onto the summit from the east side of the mountain, depending on route taken. It took us two hours from the lake to arrive at the summit and we found it to be a fairly large, flat area.
The views from this summit are impressive. The lone summit of Engineer Mtn. will certainly attract your attention, but to the east is the sea of summits that form the Needle Mountains. If you have good map reading and navigation skills, you can pick out any number of 13er summits. Once done admiring the view, either return as you came or continue on to UN13,046/N 2 to the south. We also call this South Snowdon.
Links to other information, routes & trip reports for this peak that may be helpful.