After your puppy eliminates, say, "Good Potty!" or something else that comes across as praise. Choose any short phrase that works for you, and say it in a happy, approving tone of voice. When you assign a name to the action, your puppy learns to associate the word with the act and may learn to go on command. Just don't make the mistake one owner did of using the phrase "Good dog" or your pup will start going potty every time you praise him, whether you meant him to or not. Make sure everyone in the family knows the key phrase for going potty and uses it consistently. You don't want your puppy to become confused.
Speed up the training process by making potty time pleasant for your puppy. Keep some tiny treats in your pocket so you can reward him the instant he's through eliminating (don't interrupt him before he's finished). Then, spend a few minutes playing. He'll soon learn that the quicker he does his business the sooner playtime comes. This is useful on rainy days or when you're in a hurry.