The most common worms seen in vomit or feces is the roundworm and tapeworm. Tapeworms are normally seen in feces and resemble grains of rice while roundworms resemble spaghetti. The most common worms found in dogs are: Roundworms, Hookworms, Tapeworms, and Whipworms and Heartworms
In some cases these worms are passed from the mother to the puppy, in other cases such as tapeworms, they are contracted by other methods such as ingesting an infected flea. Most over the counter medicine will only kill one or two types of worms, so your best bet is to take a fecal sample to your vet to determine the type of worms your dog may have and then decide on treatment. Dogs should be checked for worms periodically even if they appear healthy. This is so if your pet does become ill, you are not fighting a worm infestation along with a more serious problem.
For additional information about worms, see this site
Common dewormers are Panacur, which is a prescription product so you need to obtain it from your Vet and it works on roundworms and whipworms. Wormers labeled as Pyrantel Pamoate are the best over the counter medication for roundworms. Drontal plus is also a prescription product and is used for the treatment of Tapeworms, though dewormers with praziquantel work well against tapeworms. Revolution and Interceptor as well as other heartworm medications also control whipworms and roundworms. Another reason to keep your dog on Heartworm medication.
Wormers from your vet work best and are not that much more than over the counter drugs, so I would be inclined to just get a dewormer from your vet when you go.
Since worm eggs can live in the soil, you need to clean up all feces in the yard and keep them cleaned up daily, have your dog on flea preventative and then deworm at least two times two weeks apart. You can also deworm on a regular basis such as every 3-6 months.
I hope you find this information helpful.