Having just spent the night of Yom Kippur in the Avtinas Chamber, the Kohen Gadol would begin the Avodah of the day by immersing in a mikveh located above the Water Gate prior to donning the Priestly Vestments. This mikveh was accessed via [a door located on] the non-sanctified side of the Avtinas Chamber and so did not possess Courtyard sanctity.
Yoma 31a implies that the dimensions of this mikveh were 1x1x3 amos, the minimum size of a mikveh, even though the average person is actually closer to 4 amos tall.
When he enters the mikveh, however, the water will be displaced such that it will cover the top of his head (Tosafos ad loc. "amah al amah"). Now, getting into such a small mikveh is easy. but getting out is a bit trickier (unless steps are carved into the walls). Rather than have the Kohen Gadol squeeze into this little space I decided to widen the mikveh and add stairs so that he can walk down into the water and then walk out again. In the picture below, then, the walls are set at a height of 4 amos while the water level, as well as the pipe bringing the water from the Eitam Spring, are at a height of 3 amos.
While the Kohen Gadol immersed, other Kohanim would hold up a linen sheet to block him from the view of the crowds gathered in the Courtyard below. This requires that the mikveh chamber be fully visible to the Courtyard and also have a platform upon which these Kohanim could stand. After immersing, the Kohen Gadol would wash his hands and feet from a basin and then don his Priestly Vestments, all of which would have been brought in and held for him by his attendants.