Installing, centering and aligning the rear sprocket is one of the most discussed issues on the forum.
There's plenty to read on the subject so instead of us trying to explain it, try some of the suggestions offered here > http://www.google.com/cse?cx=partner...all&gsc.page=1
And no, the sprocket isn't supposed to touch the hub. There is usually a space between it and most hubs. That space should be equal on all sides. Also there should be washers under your bolt heads.