Kelso Mountain is visible from the Gray Peak trailhead, immediately to the southwest, but the north slopes are significantly steeper and have some cliff bands, so the easier approach is to take the trail toward Grays and Torreys and access the south slopes of Kelso just before beginning the ascent of those mountains.
1 shows an overview as seen from Grays. This route is also a nice add-on on the way back after a standard Grays-Torreys ascent.
From the trailhead, follow the trail toward Grays and Torreys for about 1.9 miles, passing the informational sign and crossing the creek a bit above 12,000 feet. At around 12,300 feet, slightly before the small turnoff trail toward the Torreys-Kelso saddle and the Kelso Ridge route up Torreys, turn right and begin ascending Kelso Mountain's steep but simple grassy slopes.
2 gives an overview of the first push (photo from further up the Grays trail than is needed to access Kelso), and
3 shows what it looks like first hand just after stepping off the trail.
The summit is 0.9 miles and 900 vertical feet from here. The first slope is the hardest - push up the 400 vertical feet of this pitch to view the first of many false summits (
4). The going gets easier after that as the remaining 500 vertical feet are spread out evenly on a continuous grassy slope of 0.75 miles. Ascend to the first false summit (
5), and the next (
6), and several more (
7), until the mostly-true summit comes into view (
8). The technical summit is just behind that and has a cairn (
9).
The trailhead is visible from the summit. To descend with minimal complications and steepness, return via the same route as the ascent. To descend more directly, it is possible to proceed east off the summit and meet up with the trail (
10). However, the northeast slopes have several cliff bands and even the grassy slopes are quite steep for hiking, so it is best to traverse somewhat south until a desirable slope is found. Most of the rocks can be negotiated as Class 3, but it is tough to scout it from above. A bushwack may be required from the base of Kelso back to the Grays trail, though good routefinding can avoid this. A successful direct descent shaves about 0.8 miles off the total distance and meets the trail near 11,800 feet. The included GPX file uses a direct descent through a steep Class 3 gully and avoids a bushwack by meeting up with an old mining road.