Are sniffer dogs trained either for drugs or explosives or can they do both? Is there anything else they’d be used for (at airports or other public security areas)?
Sniffer dogs have job-specific training - drug dogs are taught to identify drugs, explosive dogs explosives, body-locaters bodies, etc. Also, explosive-detecting dogs are taught NOT to scratch or dig at their finds for pretty obvious reasons, whereas a rescue dog might be encouraged to dig for trapped people.
Sniffer dogs are trained by rewarding them with food when they find the particular item you hid in a suitcase. Give a dog food when he finds the suitcase with the weed in it, he will find the suitcase with the weed in it.
The dog’s nose is NOT specific; it detects the smells of drugs, explosives, and all the other smells.
The response IS specific; they are trained to indicate to their handler only when they detect the specific item the handler is looking for (like Annie-Xmas says).
Similar with airport dogs. The behind-the-scenes luggage dogs are trained to scratch and yelp and generally go ballistic, whereas the passenger-screening ones are trained to sit down quietly and not move when they find something.
actually got into a discussion with this with my mom recently, she smuggled a box of goldfish crackers into Japan for me (sometimes you miss the weirdest things from home…) (and no, I don’t think it was actually illegal to bring crackers into this country, but my mom is weird).
While a dog’s nose can detect a great number of things, they’re generally trained to zone in on specific smells (explosives or drugs, usually not both) and yes, they’re trained to have completely different responses depending on where they will be used (behind the scenes versus walking around an airport lobby, for instance).
On an amusing note: A customs officially at Narita Airport (near Tokyo, Japan) recently planted over a hundred grams on hashish ILLEGALLY on a random passenger’s bag as it went through customs (they’re supposed to use dummy bags) and his dog totally missed it, so the passenger went to his hotel, opened his bag, and shat a brick 
story here: http://www.japanprobe.com/?p=4693 (and yes, the guy returned it, probably though he was getting set up or something. Japan has CRAZY drug laws)
In the UK some drugs dogs are now also trained to sniff out money, because the two usually go together.
There was an amusing scene on a recent BBC documentary showing these dogs at work on the streets of London. One of the dogs went and sat himself down in front of an ATM, and wouldn’t move until he had received the reward of his favourite tennis ball.