You do all your preparations on Erev Shabbat. Keep your hair tied back over Shabbat and Yom Tov to prevent as many tangles as possible, do not put on makeup that will be difficult to remove, and try to avoid sticky substances and situations that could result in chatzitzot. You can eat normally on Yom Tov and Shabbat, including meat.
On Saturday night, after Shabbat is over, you begin your final preparations. Since it is Yom Tov and not Shabbat, you can wash one part of your body at a time with warm water, liquid soap, and no wash cloth. You should also clean your teeth as permitted on Yom Tov. (There are several opinions about how to do this. We follow the position that you use liquid toothpaste (not gel) and pre-cut dental floss. If flossing would definitely cause your gums to bleed, then use toothpicks or a rubber tip instead of floss.) At the mikveh, run your fingers gently through your hair to remove tangles, and check yourself to assure that there are no chatzitzot. You wet yourself prior to immersion either with one extra dunk in the mikveh or with a shower (check with the local mikveh lady).
When you come out of the mikveh, gently pat your hair dry but do not squeeze water out of your hair.