Actually lifting the latent takes seconds, although there is prep before hand. After the bloody iPod is photo'd, inc w/ a scale (a ruler) the pritns are often exposed to gas created by (honest) putting crazy glue on pipe cleaners in a hood (upside down paper bag) which makes the prints stand out even more. Then the print make be dusted (carbon dust applied w/ feather duster-type brush) and the print is actually touched w/ a 2" piece of tape similar to commercial Scotch tape. Lifting the tape lifts the dust that adhered to the now-hard ridges and whorls of the print (hard from the gas exposure) and the tape is applied to a clean paperboard the size of an index card.
All this can be done in the field, by an average grunt ofc.
As far as the lab, if it's a pvt citizen paying a pvt lab, turn around can be w/in a week (although realize that getting a hit depends upon the right answer already being on file*) but pol labs are usus backed up for months.
*for ex, if your blood is on the iPod but they have no sample of you to which a comparison may be made (no body, you're off posting on the 'net, perfectly alive) and they don't have your parents or some blood rel with which to make a partial comp, then they have the sample waiting for a match...they can only say it's you once they have your sample or both your bio parents.