You should teach your dog the sit command first, and once he is well-trained in this, move on to the down command. Once your dog can perform the down command, you can move onto the stay command. Begin training any new command in a quiet location free from distractions.
Tell your dog to sit. Then, show your dog there’s a treat in your hand by putting it close to his nose. Lower the treat slowly and the dog’s head should follow, leading him gently into a down position. Say “down” as he arrives into position, then praise him and give him the treat. If he ended up in a bowed position, with his back arched, then simply draw the treat forwards slightly away from him to encourage him to get into the full down position. Say “good dog” and give him the treat each time he successfully gets into the correct position.
Always say “down” in the same tone of voice, don’t suddenly change to “lay down” or any other variation as you will confuse him. Repeat the exercise patiently until your dog is consistently performing the command correctly. You can then gradually perform the exercise in progressively noisier locations with more distractions. You can also begin to give less treats and simply praise him when he gets it right.
With patience, your dog will ultimately be able to perform the command anywhere you wish, giving you extra control and keeping your dog safe, healthy and happy.