This is a project in which an ESP8266 acts as a server and an android phones sends a post request to the ESP8266. Most of the android program is based from http://allaboutee.com/2015/01/20/esp8266-android-application-for-arduino-pin-control/ with a few changes in the manifest file to ge it working on Android. It uses some deprecated API's and is only for testing purposes and should not be used for any critical applications.
The esp8266 is a standard module available online - http://www.amazon.com/ESP8266-ESP-01-Serial-Wireless-Transceiver/dp/B00NF0FCW8
The nodemcu is programmed using ESPLORER. Detailed explanation for this are available at http://esp8266.ru/esplorer/. The download button looks like an Advertisement but is actually the zip file
The nodemcu program must be saved as init.lua and saved on the ESP. THe init.lua is in the same folder as the android.