Having to be circumcised depends on which branch of Judaism you are converting to.
There are four branches: Reform, Reconstructionist, Conservative, and Orthodox.
The latter two require that an uncircumcised male be circumcised at the time of conversion.
This is done in a ceremony called a brit (pronounced briss) milah.
If the candidate has already been medically circumcised, the Orthodox and Conservative rabbis will perform a ceremony called hata fat dam brit, in which a small drop of blood is drawn to represent a religious circumcision.
Although female converts don’t have to go through anything like circumcision, all four branches require, or in the more liberal branches “strongly advise”, immersion in a ritual bath called a mikveh.
The ceremony is called a tevillah and involves totally immersing your body in the waters as blessings are said over you by representatives of the faith.