The age of sharks can be estimated using either the vertebral centra (the spindle-shaped central part of fish vertebrae), and the dorsal fin spines, if they have any.
In either case, these elements are sectioned transversally and stained, to make the internal banding pattern evident. This banding pattern is produced by the seasonal deposition of calcified tissues during the growth of the animal.
This is how the bands look:
http://na.nefsc.noaa.gov/sharks/img/age7…
Usually, the researchers use the band counts from animals of known ages to calibrate the age estimations of other individuals. Each species has their own particularities with respect to their growth pattern, and most continue to grow while they live (although at a slower rate when they're older).
Because of this, it's impossible to know the age of a wild specimen. The current record indicates that a whale shark (Rhiniodon typus) lived for 70 years, and a spur dogfish (Squalus acanthias) lived for 60 years (see source below).
BTW, here's an interesting article on shark age:
http://na.nefsc.noaa.gov/sharks/age.html
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EDIT: Incidentally, shark teeth are useless for any estimation because they are constantly being lost and replaced, thus there's no fixed amount of teeth, and their degree of wear can't be used either.