How do search and rescue dogs find bodies?

• Search dogs are trained to find missing people by following scent which is carried on the air. This is a very efficient method of searching large areas quickly and does not require items of clothing or effects of the missing person.
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What other skills do they have?

• Dogs work equally well in the dark and use their senses of smell and hearing to their fullest under these conditions. It is calculated that a dog is equivalent to about 20 searchers in good conditions and many more in poor conditions. In ideal conditions a dog can pick up a human scent from about 500 metres.
• It's not just about smell, either --dogs' superior hearing and night vision also come into play.

How strong is their sense of smell?

• Dogs’ sense of smell is about 40 times stronger than a person's. To a dog, the scent of a human is as powerful and distinctive as the smell of a freshly baked apple pie is to a person. Human beings are smelly creatures - they constantly shed dead skin cells called rafts, which contain bacteria and smell distinctly human. While it's impossible to know for sure, most experts believe that search and rescue dogs are smelling these rafts, which form a "scent cone" that the dog can easily pinpoint, when they're performing a search. Everyone's skin cells smell unique, which is how a dog can smell an item of clothing and search specifically for the last person who wore it.

Sources:
http://health.howstuffworks.com
http://www.sardaengland.org.uk/
http://www.comdens.com/SAR/choosing.html