There is no reason to postpone your immersion until Motzaei Shabbat, and there is a mitzvah to go to the mikveh as soon as it is halachically permitted, if possible. Do all of the preparations on erev Yom Tov as you normally would, and pay special attention to cutting your nails and combing your hair, as those are things you cannot repeat on Yom Tov or Shabbat.
Over the course of the next two days, try to stay away from potential chatzitzot that will be difficult to wash off with just soap and water. Before going to the mikveh, you can wash your body with warm water and liquid soap (it is customary not to wash your hair), as long as your entire body is not under water all at once. Alternatively, you can wet your body in the mikveh water prior to immersion.
You can run your fingers through your hair to ensure that there are no knots (don't use a brush or comb). If you have long hair, we suggest you put it in a bun or ponytail before Yom Tov so it doesn't get tangled. Make sure to wash off make up and clean your teeth, and do a thorough check just before immersion to assure there are no chatzitzot on your body.
B'hatzlacha and Shana Tova!