I used a Wemos D1 Mini and a relay shield for this. Soldered leads to the physical button inside my garage and connected that to the relay. Toggling the relay on then off is now equivalent to pressing the button. There is an outlet next to the garage door button, so the project is powered via a USB plug and a short micro USB cable. It runs a firmware that emulates Belmont WeMo (which is really UPnP) so my Amazon Echo recognizes it. Viola! A voice controlled garage door.

I have yet to install the reed switch on the door so the thing is smart enough to actually open and close and not just emulate button pressses.

I don't trust this setup to control mains power (look up Sonoff devices for that), but the garage opener is 12 V so I feel ok about not setting things on fire with that.