Someone will probably come along & explain this better than I, but this is my understanding of the procedure.
First, you want to wait, ideally, until the placenta is birthed & the cord is white & floppy, so you ensure your baby has everything she needs from the placenta. Then you clamp or tie (I vote tie; I'm going to crochet something special, but I have heard of everything from braided embroidery floss to a clean shoelace being used) the cord a short way from the navel, and cut through it with a pair of clean scissors.
I know the usual medical form is to clamp near the baby, then clamp a second time about an inch from that, & then cut in between the two clamps. But the usual medical form also doesn't account for waiting until the umbilicus has finished its job.
If you wait til the cord is all done, you should only need the one tie near the baby.
If you feel energetic enough, you can do a search in this forum on cord-cutting; I know there was an excellent thread some time ago. There is also a section on it in the Midwife Archives on Gentlebirth.org that you can read here: http://www.gentlebirth.org/archives/cordIssues.html
It is somewhat difficult reading, as it is the archives of a message board similar to this one, but that site is one of my main ones for birth info (If you go to the main page
of the archives, there is a wealth of info on various subjects relating to labor, birth, & postpartum care.). It can get technical at times, but is fascinating to me.