There are articles in the Journal of Forensic Sciences specific to fingerprinting deceased individuals.
Basically with fresh intact bodies the process is no different to a live person being fingerprinted. The problems encountered with deceased is rigor mortis and straightening the fingers to print then you have the post mortem condition of the body with problems associated with wet decompositon and skin slippage and cases of mummification with the digits being dry hard and wrinkled.
In the morgue skin slippage with even nails intact you can slip the degloved digit over your own gloved finger then take the print. Mummification you need to soften the digits using different methods.
If the individual does not have a police record for comparison purposes prints can be collected from personal effects and objects at the residence for example and then compared with the deceased.
Another source of information with literature search is the American Journal of Forensic medicine and Pathology.
For an historical perspective check out The Project Gutenberg EBook of The Science of Fingerprints. It has a chapter entitled "Problems and Practices in Fingerprinting the Dead"
