Charleston Peak has two trails which access it. The shorter South Loop Trail, and the scenic, but also much longer North Loop. The Trail Canyon trail is a great alternative to trim some miles off the North Loop's lower portion, and allows you to hike the scenic upper trail to access Charleston Peak.
Trail Canyon trail leaves from the parking lot's north side and climbs gradually up the canyon on a very well built trail. The trail gets steeper as you hike up, and begins to take on switchbacks shortly before you enter a regrowing burn area. Views open up in the upper sections, and soon you can see your destination. The switchbacks grow longer, and after a short distance you are at the junction with the North Loop Trail.
Once at the North Loop Trail, turn left, and continue up slope. After 1/2 a mile you come to Cave Springs, and a trough with water in it, though the water is piped from a source higher up. This water may be reliable for most of the summer, or only in the early summer when snow melt feeds it. This is the only source of water on the hike, unless you melt snow in later spring.
From Cave Springs the North Loop gets progressively more interesting and substantially more scenic. Initially, you hike through the upper portions of the old burn, which has a lot of nice bristlecone and aspen. This gives way to a spectacular forest of old bristlecone pines, steep slopes, impressive views of Kyle Canyon, Charleston Peak, and the cliffs along the hike. As you ascend, the hike only seems to get better. This is probably one of the nicest and most impressive sections of trail I have been on, and I highly recommend it.
After 4 miles of impressive hiking you arrive at the base of the peak itself and begin the final push to the summit. Charleston is an ultra prominent summit despite it's modest altitude of 11,918', so despite being below 12,000', you might feel like you are much higher. Barren rocky slopes and minimal vegetation could convince someone they were several thousand feet higher. On top, views are reported to be up to 300 miles on a good day. Enjoy them if you are lucky to have those conditions. From here, return the way you came, or descend the South Loop Trail, which goes to a different trailhead.