What kind of home treatments will cure oral thrush and how long will it take for it to be actually cured?

None: Thrush is treated with topical antifungals to the mouth. These are nystatin(mycostatin) liquid suspension-swish and swallow 4 times a day or Clotrimazole troches-dissolve one in mouth 4 times a day until the lesions are gone. For resistant cases fluconazole(diflucan) 100-200 mgs. Orally once a day for a few days will usually work. I know of no home remedies that work for thrush.