In theory, you should still have your normal period if your tubes are tied, but your chances of getting pregnant are greatly reduced. However, there have been reported cases of failed surgeries that often lead to ectopic pregnancies. It is best to have a lengthy talk with your gynecologist before choosing the best birth control method for you.
You get a period, but you can't get pregnant. Your period comes from the uterus, which is still intact and functioning. What is done is the tubes which send the egg to be fertilized are cut and tied, so the egg can't get to where it needs to go. It always works, unless the doctor is a fraud.