Making something actually happen with switches

Let me start here: the more info you give, the better the answer will be, for future reference, this may be helpful: How to ask a good question / Help Us Help You

Ok off to your question. In principle openHAB works like this:
device <=> binding <=> thing (and via channel) <=> item
There are several section in the docs (Introduction | openHAB) that explain all of that.

The scheme above works for zigbee and for mqtt; you can then connect the events (state changes) happen to one item to a second (or more) items by using rules (Textual Rules | openHAB).

Going by your question, you may want to start reading from the beginnings in the docs: Introduction | openHAB to get really familiar with all concepts as there are many nuances and additional features; to get an overview will be critical and you will only frustrate yourself when you try take shortcuts. In any case, make sure that you fully understand both ends: zigbee and mqtt. If you got them working already, great, then you can focus on rules and understanding the event-driven nature of openHAB and how to read and set states of items.