OK I admit I know nothing about this stuff but I know there are some geniuses on FR concerning this subject since I myself am a genius on other stuff. (Said with great humility of course.) Anyhow how do they determine that this thing is 13 billion light years from us?
By looking at the color spectrum of the light. Colors have wavelengths and there is a way of measuring the redshift of the spectrum that is detected.
More info here:
http://www.esa.int/esaSC/SEM8AAR1VED_index_0.html
http://en.wikipedia.org/wiki/Red_shift
The Doppler red shift of the light from the object...IIRC
Mostly they used redshift, although sometimes they can see an object inside a galaxy that is of a type they know fairly well and can get the distance a second way from that. The redshift is the actual data and the distance is the result of a pile of assumptions.