Sit, Down, & Up:
We use the Food Lure technique to first teach these commands. Some of these things may have already been learned, that’s great. You can use the dog’s current knowledge of each cue and progress further to adding hand signals. Each command should have its own word and hand signal.
Teaching a dog to "Lay Down."
For both the "Sit" and "Down" commands, we use a food lure. For Down, start the dog in a Sit position and reward for this. Then slowly move your baited hand (hand with a food reward already in it) from the dog's nose to the ground, pause for a second, then pull forward and out. Make sure you move very slowly keeping the dog's nose "attached" to the food reward. The reason we pause for a second when you hit the ground is that about 50% of dogs will actually slide backwards to lay down instead of moving forward. Be sure to move from the dog's nose downward but staying close to the dog's chest. Pause here and wait to see if your dog slides backwards. If not, slowly pull the food along the ground forward. Wait until your dog's body touches the ground then immediately say, "Down...Good!" and give the reward. Repeat this until your dog is doing well and seems to have a good handle on the Down command, then you may start adding the word before the action.
Other helpful Blog articles:
Anti Jump Training
Helpful Ways to Exercise your Puppy
Training Come When Called