After your dog has mastered the sit, it's time to introduce the down.  However, before we begin, let me say that the down position is a submissive position and many dogs feel uncomfortable if they are asked to down in an environment or situation where they feel threatened.  So when teaching this exercise make sure you do it in an area where your dog feels safe.

Start again with the dog on a leash and sitting in front of you.  Take a treat and let the dog sniff or lick it.  Then very slowly (slowly is the operative word here) move the treat straight down along your dog's chest all the way to the floor. 

Make sure your dog is following the treat and licking at the treat all the way.  If not, begin again but this time do it more slowly.  Be sure that the treats you use are something special so he will be more eager to earn it.

When your dog is sniffing the treat on the floor directly in front of his paws, slowly move the treat along the floor in a straight line out in front of the dog (it's an L-shaped pattern).  If you go slowly enough allowing your dog to follow with his nose and lick at the treat, he will remain sitting and walk his front paws out as he follows the treat until he ends up in the down position. 

If your dog stands instead of going down, it means you need to slow down even more.  You can place your free hand on his shoulders to help guide him down but be sure not to force him down.

Continue this many times.  As with the sit exercise, when your dog's elbows are just about to hit the floor, that is the time to say, "Down." 

After your dog consistently goes down when you ask, tell him to "stay" and do the same stay exercise that you did with the sit until you can stand at the end of the leash and walk all the way around your dog and step over him without him getting up.

Once sit and down are established start mixing them up.  I like to get all our dogs in the kitchen with a pile of treats.  I say sit and those that sit get treats, those that just stand there wagging their tails at me and looking goofy with their tongues lolling out get nothing.  It usually only takes two or three times before the dogs figure it out and wham all the butts hit the floor.  Some get smart and don't get up -- they get an extra treat.  Then I do the same thing with down and I mix it up sometimes doing two sits and one down and vice versa.  Try to keep them thinking.  The dogs love it and often start sitting and downing on their own throughout the day in order to weasel a treat from me -- they always get one, too!