The suggested brush is just a hard bristled brush you can buy at any drug store.
There are specific instructions, but they are short (borrowed from the website I link to below):
"I believe you should start the dry skin brushing session by starting at the area around your armpits, then brush your stomach in a clockwise circle, then brush your upper leg area. This stimulates the areas closest to the main lymph nodes. Then, to keep it simple, you can start at you feet and sweep up the legs in long, light brisk movements. Brush your arms with an upward motion, moving towards the heart All skin brushing movements should be towards the heart, to encourage the return of blood and encourage lymphatic flow.
Pay particular attention to the cellulite-prone areas like your thighs... The whole process should take two to five minutes.
Make sure the brush you use has natural bristles. You should ideally dry skin brush before every shower."
Video on this site, I had this women perform the lymphatic drainage massage on her site too, love her!