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."
With your dog sitting, kneel in front of your dog so that you are facing each other. Take a treat in your hand and put it a few inches in front of your dog's face. Slowly bring the treat down to the ground. Bring the treat slightly forward as you are bringing it to the ground (a dog's face will come slightly forward when they lie down). This should make your dog follow the treat to the ground, causing them to lie down. If your dog just drops its head, try bringing the treat down slower and a little further away. If your dog gets out of the sitting position and walks to get the treat, bring the treat down straighter and not so far forward. Make sure you repeat your trigger word throughout the training process.
Once your dog lies down be sure to reward them by speaking happily, repeating the trigger word, and giving them the treat and lots of love and affection. Repeat this several times until your dog is able to lie down without having the treat guiding them to the ground. Your dog should begin to lie down solely from hearing the command to do so. 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 not just sitting down.