How it works: A small chip encased in surgical glass (the whole thing is about the size of a grain of rice - the glass is what is used with pacemakers) is injected deep into the dog's subcutaneous layer - typically between the shoulder blades. The chip is coded with a number, and when a scanner is passed over the are where the chip is embedded, the number displays on the scanner screen. The number is registered (with the manufacturer of the chip, and if you want the AKC), and if a stray dog is found to have a chip, the person who is registered to that number is contacted. (There was just an incident a couple of days ago in Canada where a lost dog, who was found and was chipped, was unable to be reunited with its owners because the chip company did not have their number on file. The breeder of the dog had called just a few weeks ago to verify all of the information on their chips, and everything was correct, yet when the dog was found the information was nowhere on file. Disturbing - but those of you who have had your dogs chipped might want to make a habit of verifying the information regularly!).
Anyway, as I said my puppies are chipped before they go to their new homes. The chips are registered in my name (I purchased them from the chip company), and if the new owners choose to enroll in a recovery program (either the chip manufacturer's or the AKC's) they can. If they do not, and the dog was lost, the chip company would contact me and I have records as to which chip belongs to which puppy, and the owners' contact information.
There have been stories about the chips migrating, but most of those happened years ago when they were new to the market. Chips probably do sometimes migrate today, but I feel that the occurence is rare.
There are also those who feel that microchipping dogs is just a ploy to get us used to the idea, so that someday the government can begin microchipping humans (and indeed, they are doing trials of it with Alzheimer's patients.) I'm not about to get into that discussion here

but it's something to think about.
How much does it cost? Well, I think that to have a vet implant a chip they provide is around $35 US. I bought my own chips, which cost I think around $9 each (I bought 50), and just have my vet implant them (I can't deal with that huge needle yet!) and I haven't been charged for it (even at a clinic I've never gone to before.) Registration with a recovery program is around $12 (I think).
I do feel that my dogs are more likely to be recovered with the chips in, plus I got a sign for my fence stating that all of my dogs are chipped which may deter thieves. I think the benefits far outweigh the risks in this area.
Julie