Question what there an important reason on why you resigned from that job? Or did you just want a vacation the sooner you talk the better or go in person forget the letter good luck.
Depending on the circumstances and the type/ size of the company, you need to decide whether to write or call, and whether to go to your boss or someone else. The main thing is to make it clear why they should take you back, but also if there was any dispute or problem, why there will no longer be a problem. There is some very good advice at collegejournal.com.