There are two kinds of tapeworms. For simplicity we will refer to them as the "flea" tapeworm and the "rodent" tapeworm.
These are those nasty little segmented worms you see around a dog's anus. The adult worm is actually 6 inches long or more and lives in the small intestine. As the worm ages, new segments are produced and the older ones fall off. These are the ones you see in stool or around the anus. The segments are about the size of a grain of rice and while fresh will still be moving. Later, they dry up and look like sesame seeds.
Rodent tapeworms are acquired by eating (as you may have guessed) the internal organs or rabbits, rodents, and some other animals. The life cycle proceeds similarly to the flea tapeworm at this point.
Tapeworms don't usually cause much harm to the host but they often create an "emergency" when discovered by an owner simply because of the gross factor.
Tapeworms are rarely seen on fecal exam because the segment must first break open to release the eggs. Most commonly tapeworms are diagnosed by visualization of the segments. Both kinds of tapeworms can be treated with praziquantel, only the rodent tapeworm can be treated with fenbendazole. You only need to deworm for tapeworms once to eliminate them but a dog can potentially (not all fleas carry tapeworms) be reinfected every time it consumes a flea. Therefore, flea control (or minimizing hunting of rodents for the other variety) is necessary for tapeworm control.
Humans can theoretically be infected with a tapeworm but they would need to get it the same way the dog did-by ingesting a flea, or even worse, rodent guts.