Easiest method is definately the 'shrimp in' method. I used this method and was cycled in 4 weeks. Drop a shrimp in and just test the water every few days... thats it. Too easy. As for speed... the ammonia method is pretty fast I hear as there is no waiting for food to break down to create ammonia. I wouldnt bother adding food aswell as ammonia as there is no point, the food is only added so that it will break down and create ammonia. No need for this if you are already dosing ammonia straight in.
I got all my info from the cycling sticky on this site and it worked a charm but if you need any specific help just holler.