Easiest access to Center Basin is over University Pass. Start from the Onion Valley Trailhead and take the trail to Robinson Lake. From there it is cross country up the canyon. It is a talus slog all the way to the base of University Pass, though there are a few spots were you can walk on the sand in the very bottom of the canyon. Scramble up University pass. This is the leftmost notch. Stick to the edge, as the middle is full of loose sand and rock. Descend the other side using caution. This side is very steep and loose. Center peak becomes obvious from the top of the pass. It is located directly in the middle of the basin towering over Golden Bear Lake. Once at the bottom of the west side of the pass, veer left and head towards the east side of the peak. There is a small use trail you can pick up and follow. You will have to cross the creek to get to the base of the east side.
Follow the small use trail around to the east side of the mountain. The trail climbs straight up the mountain for several hundred feet. This portion is pretty sandy and loose, though you will not need to use your hands. The trail disappears when the terrain turns rocky. I found the rock to be stable from this point on. Continue up, weaving through the rock. There are a few ducks and footprints to follow. You will need your hands for balance but the route to the top does not exceed class 2. If you lose the main path, do not worry. There are several variations you can take through the talus. The last 50 feet or so are the most challenging, but the view from the top is worth it! The summit block is a huge boulder that sits about 12 feet higher than everything else. It is class four and has a decent amount of exposure.
Hiking boots and a coat for the top.