I have 208v 3 phase in my building and to my machine, but I need 120v to run my conveyor. How can I wire it to get 120v off the 208 3 phase wires?
I used the green, white and black wires and checking from the ground to each leg I get 125v but from leg to leg I get 211v. Can someone please help me?

Well, you should have blue, black, red, white and green or taped as such. Your missing the white wire. A neutral has to be pulled from the 3 phase panel or the load should come from a single phase panel.

3 phase motors don't need the neutral to function or be wired properly. You just need the three phases and protective ground. Depending on the equipment, neutral may be run.

What you measured is correct.

Sometimes it's advantageous to use a 120 V control voltage or even a 208 control voltage, it just depends on the equipment.

The conveyor should have been purchased or wired for 208 with controls being at a lower voltage derived from a small control transformer.

It's impossible to consider all of the possibilities without knowing more. I would suggest hiring an electrician.

how to get 120v from 208v
You don't without a neutral.

This is NOT a DIY job. Working in a commercial setting on three phase should ONLY be done by a qualified electrician.