Controlling LED Strip with Arduino, Through Wifi Using ESP8266

hello, I have just started working with the rduino and i'm enjoying pretty much so far. I have taken up a personal project of making a table lamp using abt 3metres of White LED strip which will be connected to an arduino. i'l be using a 2A 12V power supply for the LEDs.

the problem i'm facing is how to use the wifi module ESP8266 to control the lights. i want to make a basic mobile app that will have an on-off button and a intensity slider to adjust the ntesity of the light. Please help me in knowing how exactly to do this with an ESP8266 (if u recommend another way of doing this through wifi, please give ur suggestion) i want to know what else i'l be needing for the project other than the earlier mentioned. i will need a TIP120 transistor right? and i do have a breadBoard for now.

i plan on using this module http://www.ebay.in/itm/like/231699107906?aff_source=Sok-Goog and not the PCB mountable one...Please guide me on this