What is the best way to clean the carpets when house training a puppy?
You might want to invest in a small carpet steamer. I bought one a while back for about $100 from Bissel and it’s been well worth the investment for other times when I needed to freshen up the carpet (pets over the years can have new smells that grace your carpet periodically).
For spot cleaning, try Resolve or Krud Kutter (both work great on carpet). The key is to get the soiled spot cleaned up quickly so it has less time to settle into the carpet.