How do I replace switches that control 4 different ways

I don't understand the question. You remove the switch and install a new one.

The trick is determining what type of switch it is.
In the wiring scheme the first and last switches are "3-way" switches. ALL the switches in between are "4-way" switches.
This is not to say they will physically be in this order. It all depends on how the electrician wired it.
I know this is confusing but that's just how it is.