A short climb on some faint trail segments, and a little bushwhacking through scrub oak on a south-facing slope.
Either drive south on (Lower) Gold Camp Road from 26th Street or 21st Street (at the top of the big hill) in western Colorado Springs, and continue west past where the pavement ends and the road enters North Cheyenne Cañon Park, or drive up North Cheyenne Cañon, past Helen Hunt Falls and to the "4-way" parking lot, and then back, east on Gold Camp Road, through tunnel #1. Either route leads to the Capt Jacks trailhead parking area, just east of the tunnel.
This route begins as the Capt Jacks TH, just east of Tunnel #1 on Gold Camp Rd. From there, take the road west to the east end of the tunnel. On the south side of the road, look sharp for a faint trail which heads south up the slope. Near the crest of the ridge (through which the tunnel is bored), turn sharply right (north) and follow the trail back, directly over the tunnel.
Shortly thereafter, the trail disappears. Stay to the right (east) of the ridge crest, and continue climbing through scrub oak, eventually switchbacking up to the ridge crest near the rocks which can be seen from below.
At that point, a faint trail along the ridge crest can be picked up, still heading north and a little west. Follow this trail over two small ridge points and, finally, to a third point marked by some prominent rocks. From there, turn west (left) and drop a few feet to a saddle, where you intersect the trail corkscrewing around Mays Peak. The trail quickly turns directly uphill on the north slopes, and leads directly to the summit.
The hardest part of this route is the bushwhacking through the scrub oak, both on the way up and on the way down. You will probably not follow exactly the same route in both directions, but don't worry: The trailhead below can be easily seen from most of this sectiton.
Whatever the season dictates for a short hike in the mountains. No technical gear is needed; this is a walk-up.