Follow the directions in the article.
Oops looks like it does not tell you.
Boot from the thumb drive and choose your formatted hard drive as the destination and install as usual.
You can just run it from the desktop already booted in. I used Lion Diskmaker 2rc2 to make an install USB and used it to intall 10.8 on four of my Macs. No problems whatsoever.
It worked! The stick is MUCH, much faster than a download or DVD. In less than 30 minutes I erased my HD and installed a fresh install of Mountain Lion.