My puppy has white worms. How do I treat him and disinfect my home?

Oh my. Poor Gunner. If these are small like white rice then they are likely tapeworms. Tapeworms are not infective once they are dried up; therefore, you can use normal everyday cleaner to clean the area free of the worms. No special requirements needed, since they are not infected once they are dried up. If you do see a live worm, then wear gloves to remove them from the area, then spray as needed. Good hygiene is the best way to prevent infecting yourself, which requires you actually ingesting a live worm.
A tapeworm medication (i.e. Praziquantel, Drontal) should be started right away to rid the worms in Gunner's system. Also a flea preventative (i..e Bravecto, Nexgard, Trifexis-heartworm and flea) is needed to prevent re-infection, since Tapeworms come from ingesting a flea.

If the worms are Roundworms, then the same recommendations apply, except Roundworms look like angel hair pasta and don't come from fleas, but instead from the environment and in-utero infection is common. These are treated with a broad spectrum dewormer (i.e. Pyrantel Palmoate or Fenbendazole).

I hope you can get Gunner free of his parasites soon and get him on the right track towards healthy living. Take care of yourself and especially any young children that may come into contact with Gunner, as they like to stick their hands in their mouths without washing first (typical way people get infected with worms). Best wishes.