Take your dog outside every two to three hours and after naps and meals. Puppies tend to eliminate after playtime, so you should also take your dog outside then. If your dog eliminates, click the training clicker and give your dog a treat along with lots of praise. This helps the dog to develop positive associations with urinating and defecating outside. While you don't need a training clicker, the sound of the clicker, when used consistently, will strengthen praise and training for your dog's positive actions. Walking your dog as frequently as possible not reduces accidents, it also helps fight obesity, a common ailment among Basset Hounds.
Keep your dog in a crate when you are unable to supervise your dog. Dogs are unlikely to soil small areas in which they must sleep, and crate training helps dogs learn to control their bladder and bowels. Dogs should not be kept in their crates for longer than a few hours, as this increases the chances of an accident, and makes future mishaps more likely. This is especially true for puppies.
Take your Basset Hound outside immediately if they have an accident. This encourages an association between eliminating and being outside. Next clean up the mess with an odor neutralizer. Basset Hounds were originally bred for their scent-tracking ability and are strongly guided by their nose. If your dog smells urine or feces in the carpet, soiling the same spot again is much more likely.