Hike up the Robinson Lake trail until you are right below Independence peak's west face and leave the trail and start slogging your way up the class 2 west face. This spot is around 10,000 ft along the trail. There are some use trails at first. You'll eventually want to head for a notch that is south of the summit. There are some class 3 moves going up to the notch - mainly to get around a large boulder. See the photo page, there is a picture where you can see the boulder in question. From the notch, continue at first on the west side of the ridge, but you'll drop down to the other side of the ridge very soon. Proceed along the ridge and up to the summit. There is more class 3 here.
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The West Face route you want looks "reddish" from below (as opposed to a whitish scree slope just to the south). From the notch, I found the most natural way to go was to immediately get on the north side of the ridge and proceed to the summit.