A lot of these WiFi electrical outlets use ESP8266 modules. The modules can be flashed with custom code to perform on/off/status/etc by accessing the device directly via IP.
A google search for ESP8266 outlet will give you several sites where people have already done this and have published their code.
Some other options are to use an ESP8266 and a relay, a prebuilt ESP8266 relay board module, a raspberry PI and relay, etc.