There are several methods that can be applied to dead individuals or museum specimens (skeletons). In the latter case, the analyses of tooth wear or baculum (os penis) in carnivores, for instance. The analysis of the dry weight of the eye lens or the analysis of the growth of the long bones are others.
This review is old, but recent literature on this topic, as to my knowledge, is scanty:
Morris, P. (1972). A review of mammalian age determination methods. Mammal review, 2(3), 69-104.