There are two different kinds. You can do it the way you described which is traditional scarification, and probaly the most popular, it's mostly for stuff that is thicker lines and for the ritual of it. Especially if you plan on keeping the skin to cook/eat or whatever you desire.
The other way is dermabrasion scarification, which is more like a tattoo and more controlled. With this the skin isn't cut off, it's just destroyed. They take a tattoo gun and dry run it really roughly over the design, destroying the skin with the needles. Or sometimes they take a dremel tool which is becoming really popular due to it's ease of purchase, that way you can do it yourself.
This is a dremel style dermabrasion....