Down is a good second command to teach your dog. It can help stop a lot of behavioral problems your dog can develop like begging, jumping up on people, and running after other dogs or people. Down can be originally taught from the sitting position. It is an easy transition to start teaching "down" after your dog learns "sit."
Starting from the sitting position face your dog. Have a treat handy but not in your hand (you will need both of your hands free for this technique). Put one hand on the back of the dog's neck between their shoulder blades. Grab the dog's front paws with your other hand. Simultaneously, push down on the dog's back and pull their front legs straight out in front of them (don't be too forceful). This will cause the dog to lie down. Repeat your trigger word throughout the entire movement to get your dog to lie down. Once they lie down happily speak to your dog, repeating your trigger word, their name, and telling them they did a good job. Give your dog a treat and some love and affection. Repeat this several times, until your dog lies down after being told to do so without being forced. Once your dog lays down on the first command many times, try to get your dog to lie down from a standing position. Your dog should learn to lie down when it is standing up and not just sitting down.