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.

I made a similar thing, and I chose wifi because the garage was simply too far for wires. It's a simple build with a relay over wifi.

Why would you use wifi rather than radio? encryption?

For me: because it requires the least amount of hardware and also works with Amazon Echo for voice control. With a different type of radio, if you still need it on the internet, you have to somehow bridge it, which means more hardware.

Yes, and reliability. TCP gives you a lot of nice things.