The Wagonwheel lake trailhead is located near the Staircase Ranger station of Olympic National Park. It is a laborious hard hike of 3,100 feet in 2.8 miles to reach wagonwheel lake. From there it is another half mile to the summit of Cub Peak, gaining over 600 feet.
The Wagonwheel Lake trail is a rough trail with many switchbacks that cut straight up the side of Copper Mountain. It is a rather laborious hike with limited views. The last mile is particularly steep, going through thick montaine forest until finally coming out onto an open avalanche slope where views of Mt Lincoln, Mt Cruiser, Mt Skokomish and Mt Stone can be had. Shortly afterwards the trail crosses a small creek and then climbs a short bit to reach Wagonwheel Lake, a small rounded lake beneath Copper Mountain. From here the trail forks. One trail heads south towards the lake and the other continues straight and east towards Cub Peak. From here you switchback up a slope for several hundred feet, gaining lots of elevation. The trail is fairly faint and difficult to follow but not impossible to see.
Upon reaching the top of this there is a meadow ridge. Straight ahead above several jagged summits of rock is Cub Peak. Cross the meadow and continue heading east. The traverse across these jagged rocks is fairly tricky and requires scrambling to get around or over these outcrops, which are never more then 10 to 15 feet high. Upon passing several of these there will be a narrow ridge, with scree falling off on both sides. It's about a foot or two wide at this point. Scramble across this and you will be directly beneath the main summit. From there it's a scramble up about 40 feet until the summit reached.
This is basically just a hike with some scrambling so I'd only recommend a helmet in winter conditions for safety on the traverse.