How do you install an air conditioner in a casement window?

i don't know.

This is done using a portable air conditioner. These come with a single or double exhaust hose. All of these are on casters so that they can be (1) moved between rooms, and (2) emptied of water for those units that are not self-evaporating.

Some of them come with inserts that are designed to fit in the window, none of them in my experience work well with casement windows. You have 2 options (1) cut a piece of plexiglas to size to fit the open casement window and cut a 4" to 5" hole(s) to fit the exhaust hose(s), or (2) an exhaust port can be specially made that is used instead of going through the window (through the wall, for example).

Generally these units are (1) Heavy - around 100 lbs, (2) not that efficient - less than 10 seer, (3) expensive - more than $400, (4) power hungry - usually in practice they require a dedicated 20 amp circuit. But they do work.

A viable alternative that I have used in the past is to replace the window with a double hung. Then a standard window air conditioner can be used.