There are many ways to teach a dog to do a "down" - to lie down flat on the floor.
I use a method called "luring". I ask a dog to sit and then with a treat in my hand I place my hand in front of the dogs face and "lure" him into a "down". When he lies down I give him the treat.
When I am luring I make sure that at all times the treat is right next to the dog’s mouth, in fact he can lick it, he just can’t eat it. He doesn’t get the whole treat until he lies down.
When it comes to luring a dog I use something I call "The Edison Approach". There are a thousand ways to lure a dog into the down position.
A large percentage of dogs will follow your hand if you move it straight down to the ground and with your hand at ground level, slowly move it out along the ground enticing the dog to follow it until the dog is lying in a down position.
There are dogs that won’t get into a down for this though. They’ll stand up and follow your hand. First, check your hand position. If you weren’t holding it close enough to the ground you were actually luring your dog to stand up and follow the treat.
Make sure that at all times the treat in your hand is close enough to your dogs mouth for your dog to lick it.
If your hand is in the right position, close enough to your dogs face, then try moving your hand in different directions. Some dogs learn down best by luring straight to the ground and then to the right a bit rather than straight out. For some it’s to the left. It goes without saying that you have to use what your pet (not you) thinks is a good enough treat.

Small dogs learn this best from a height; either up on the couch or on a table. Don’t get frustrated, it’s kind of fun to figure out what works best for your dog.
The sequence I use is to give the hand signal for down. The correct hand signal is your hand straight up in the air. I don’t know why this is the correct signal but I like it for a few reasons:
#1. Most people point to the ground for down and actually crouch down to the ground. This can be kind of amusing when the owner is doing a down and the dog is standing there watching.
#2. If my dog were across the street I would not ask him to come to me, I would ask him to do a down/stay so he would be safe. I’m not sure he would see the typical finger pointed at the ground. I know he’d see my arms raised. (He may not be able to hear from across the street so he has to be able to see my signal.)
I give the hand signal (whether the dog recognizes it or not), I say down and then I lure the dog into a down, and then reward. 90% of the time I lure a dog only 3 times and he gets it.
Then I just give the hand signal, say "down" and wait. This is another reason I like the official down hand signal. I will wait with my arm raised until it feels like my arm is about to fall off. If I get to that point it just means I haven’t taught the dog "down" well enough.
Many, many owners will give the hand signal, say "down", wait two seconds and say "See, he won’t do it!" The raised arm hand signal gives a bit of a time line to go by. (If your arm hasn’t started to ache you haven’t waited long enough.)
Also, while you are waiting for your dog to do a down ignore everything else it does. If he jumps on you ignore it, if he walks around you, ignore it. Keep your arm up in the hand signal and quietly repeat down.
Forget everything you have ever heard about repeating a cue to a dog. Many trainers think you should only say it once. Have you ever learned anything the first time someone explained it to you?
And you supposedly have the big brain! Give your dog a break and remind him what you are asking for.
Now, I have been doing this for a long time and I can judge pretty quickly how well a dog has learned something. If you are unsure at all, use the luring method for 3 days rather than 3 times. It’s much better to go slowly than to rush it and confuse your dog.