The only way your pet can get the most common tapeworms is by swallowing a flea that has the tapeworm larvae.  Juvenile fleas eat the tapeworm eggs and in turn infect your pet when ingested.  Tapeworms are actually quite long but segments containing eggs break off and are passed in your pet's stool.  These segments look like small pieces of rice in the stool.  You will need to visit your veterinarian for treatment.