Just like a regular coin door, it'll have a switch at the bottom with .250 QD contacts labed NO, NC, and COM.
Common is your return path (or Ground).
NO is for Normally Open contacts, NC is for Normally Closed. You'll be using Normally Open.
One wire from Ground on your Encoder goes to COM. The other wire from the COIN or button input goes to the NO connection.
When a coin is inserted, button is pushed. Viola.