What exactly do you do and say when you fall Korim on Yom Kipur?
As far as I know (there may be variant customs):
In Aleinu: kneel at כורעים, prostrate (head and hands to the ground, while still kneeling - essentially, a fetal position) at ומשתחוים, stay that way until הקדוש ברוך הוא, and then get up.
In the Avodah: kneel at כורעים, prostrate at ומשתחוים, and stay that way until לעולם ועד.
[In all cases, if it's a stone floor, halachah mandates that you put something on it beforehand (such as a towel), because one may not prostrate oneself on a stone floor outside of the Beis Hamikdash. Some have the custom to do so regardless of what the floor is made of.]