[general8bitso]

Battery depends more on what you are doing.

Most boards and sensors use either 5 or 3.3 volts DC.

You can put the device in a sleep or hibernate mode and have it only connect to wifi periodically or when triggered.

Also, using encryption, like WPA2 increases battery use.

[beardyw]

The esp8266 module itself runs at 3.3V but seems happy with a couple of AA batteries. Tried with CR3032 but it can't deliver enough current. After all, it is doing WiFi.

[general8bitso]

Google ‘joule thief’.