Conditional Logic via REST API

Guys,

We are in need of some documentation or a walkthrough on how to use conditional logic. We are being told that it can be done via your system but I'm not seeing anything online that helps describe how to make it happen or what to do.

Do you guys happen to have any documentation or examples I can use to try to make it work with our system and does anything need to happen, system wise, for this to work?

Thanks!