The easiest way I've ever seen to teach down is called the 'armchair down.' A trainer I took a class from showed us this and it worked so fast and easy for my newest addition, Pecos, that I was amazed. It also works for cats, I used it with my youngest, Ruby.
First you need to teach your pet what the clicker means, but that shouldn't take long, just a few sessions of click/treat. Once you see the animal is paying attention, you can work on the 'down' behavior. (See our Clicker Training Instructions)
Now that your pet 'knows' that a 'click' means he will get a treat, gather up your clicker and a bunch of soft treats, put the dog on a leash, or work in a small room with a door you can close, and take a seat in your favorite chair. You can even watch TV while you do this. Now take a seat and just wait for your pet to lay down.
Don't say anything, don't worry, just wait. When the animal finally calms down and lays down, click and toss a treat at him, then wait for him to settle and lay down again. It's fine that he got up to get the treat, this is what we want, it sets the animal up to try and figure out what got them the 'click.' It may take 5 to 10 minutes the first time and even the second or third time, but soon you will start to see the animal making the choice to lay back down.
Click and treat each time he lays down. By tossing the treat out to the side and making him get up to retrieve it, you are setting the animal up to make the choice to lay down again.
You should see a point where the animal quickly goes back to lay down and you are giving the click/treats in fairly rapid succession. At this point, you should be able to tell if the animal is going to lay down, you should be reading his body language easily and be able to recognize the movements he makes as he starts to lay down. Do a few more click/treats for the 'down' to make sure he is repeating the behavior consistently, then just before he lays down the next time, say 'down.' I also urge you to use a hand signal at the same time. Using a flat hand with your palm facing the floor, make a short downward motion.
By giving the 'cue' just before the animal does the behavior, he will start to associate the word/hand signal with the 'down' behavior.
Soon you can start giving the cues a little sooner to see if he is responding to them and it won't be long before you can ask for a 'down' and your pet will lay down!