My friend's dog uses the restroom on his carpet a lot, and he's already tried lots of methods to get it to stop. Does anyone know an effective way to toilet train a puppy?
I've had a lot of success with crate training.
Dogs won't relieve themselves where they sleep or eat. Keeping them in an enclosed area and bringing them outside when they have to go to relieve themselves teaches them where it's OK to do so.
I recommend buying an expandable crate. You want to give them just enough room to stand up and turn around, but not enough that they'll start going in the corner. As they grow you can increase the size of the crate accordingly.
The Humane Society has some great info on crate training.
@Paperjam is right: crate training is probably the most effective way to quickly housetrain a puppy.
I will also add that routine is incredibly important when house-training a puppy.
Take your dog out on a schedule: the same times, every day. Also try to take them out shortly after they eat: puppies might have to go as shortly as 30 minutes after a meal. You want to set your pup up for success.
Lastly, let me emphasize that accidents will happen. It's natural, it's frustrating, but it's not the end of the world. What you don't want to do is scold your puppy, or "rub their nose in it". Dogs don't really learn that way, and usually just ape your emotions to appease you when they can't figure out what's wrong. It's better to try and prevent such accidents from happening, rather than reacting to one that's already transpired.