How do I get a totally white background without the subject being too bright?
We do this all the time. All you need is a white wall and plenty of light.

The goal is to light the wall far brighter than the subject in front. You want it so that when the subject is properly exposed, the wall behind them is vastly overexposed/blown out, thus losing any details/texture on the wall. 

It helps to keep the subject at a distance from the backdrop.

Here's the last shoot I was on using this technique: