Hold a food treat with your hand closed around it in a fist.  Wait quietly until your puppy finally moves his mouth away for a nano-second.  Click, then release the treat to him.  Repeat 5 - 10 times.  You will notice the puppy "getting it" more and more quickly.  Once he is demonstrating the behavior fairly reliably, you can say the cue "Off"  just once, in a friendly way before you hold out your fist.

After another 5 or so repetitions, raise the standard by requiring the puppy to wait for a count of two before you will click then release the treat.

After another 5 repetitions, raise the standard again, so that the puppy has to wait politely 'til you have counted 5 before he gets the treat.  If he mugs your hand before the 5 seconds is up, no click and no treat. 

Once he is  reliable, you can use the cue, Off, and the food release, without the click.

To teach the "sit", conceal a lure in your hand, place the lure on the puppy's nose and move your hand back over the puppy's head to just above his shoulders.  As the puppy's head tips to follow the lure he will go into a "howling at the moon" position, and then tuck his rear into a sit.  Don't hold your hand so high that the puppy jumps, or so low that the puppy stands.  Do not force the puppy into position.  As soon as his rear touches the ground, give him the food reinforcer and praise him.  Once he is smoothly following the lure, you can start giving the “Sit” cue, just once, before you lure him into the sit position.  

To Lure the Down , have the puppy sit by your side, rest your left hand (which is also holding the clicker) gently on the puppy's back and put your right hand, with a food lure in it, on the puppy's nose. Lower the treat from the nose to the toes and then slightly forward along the ground, as if you were writing the letter "L". Click when the elbows touch the ground, then feed the Lure to the puppy. Do this 2-3 times.

Now hold the food lure in your right hand, but be sure to hold the treat so that your thumb is holding it in place against your palm. With your right hand palm down, move the lure from the puppy's nose straight down to the ground.  (This is just what your Down signal will look like later.) You should no longer need to rest your left hand on the puppy's back. As soon as the puppy's elbows hit the ground, click, then release the food treat. Repeat 2 or 3 times.

 Now, put food in *both* the clicker and the Signal Hand.  Lure the Down, as above, but, after the click, now feed from the *other* hand (the hand w/ the clicker), and do *not* give the food from the Signal Hand. The dog learns, "Hey, I'm not getting it from the Signal hand, but I'm still getting a reward!" Repeat this twice.

Then quickly move to the next step, which is to repeat with *no* food in the Signal Hand. Click, and treat from the non-signal hand. By the time the dog flops down and realizes that there's nothing in that signal hand, you have Clicked and Treated again from the non-signal hand. The dog begins to understand that it's *not* about "following food", but about responding to the signal, getting the click, and being "paid" for the click. 

If your puppy hesitates before lying down at this stage,  just wait quietly.  Do not repeat the command, do not click, do not reward. Wait.  He has practiced, and he is learning that elbows-on-the-ground is one way to motivate humans to feed you.  He may experiment with other behaviors, but in a little while, he will Down.  When he does, click then treat.

Once the puppy is reliably following your signal hand, give the cue “Down" just once, before you signal for the behavior.

OR, To Capture the Down

Take one puppy, ideally a little hungry and a little tired, and working in a quiet place initially, quietly wait, thumb on clicker, for the puppy to lie down.  Don't coach, just wait.  

When the puppy downs (elbows on floor) click, then toss a treat past the puppy so that he has to get up to get it.  He will probably start to mug you for treats.  Ignore him.  Wait quietly 'til he lies down again.  Click, then toss a treat.  Repeat 5 or 6 times, then change your position and do a few more.  Many puppies will now be actively trying to get you to click.  They may be staring at you then staring at the floor.  They may be shifting their body about, trying to figure out what makes you click. Some puppies will already be throwing themselves into the down! Others won't have it figured out yet.  No problem, just work a bit more.  If necessary, repeat this procedure at 2 or 3 more sessions.  

Once your puppy is dropping repeatedly, rapidly, deliberately, you can start to give the verbal cue, Down, just before the puppy goes down.  
 

You can lure the behavior:

• Using you as lure: i) Walk briskly;  ii) use a  "vocal Lure" like "pup-pup-pup" or a whistle; iii) bend slightly down as necessary to encourage the puppy. (When humans get littler it seems to mimic the way dogs play-bow to one another, and will generally encourage the puppy to interact, to follow, to come...)
• Using food as a lure: show the puppy the treat, then hold your food-containing hand flat against you, so he tracks it, but doesn't jump for it.

• Make sure to keep the leash slack-- if you pull you will make the puppy pull!
• Initially ask for only 3 or 4 good steps before rewarding, then repeating, rewarding, then repeating... Once the puppy has been successful at following you with a loose leash 4 times, ask for more, maybe 6 steps.  You can raise the standard several time sin one session, usually, so start small and successful, then gradually work for longer and longer distances.

Or, you can capture the behavior.  Watch the puppy closely, and whenever he is in position at your side, click and deliver a treat.  At first, be outrageously generous with your snackies.  Soon you will be able to raise the standard and add more steps.

When the puppy pulls, stop dead.  Wait 'til he offers you slack, then instantly click/treat and go! (Dog Trainers call this game "Red Light-Green Light")

You can also practice Ping-Pong Come

Ping Pong Come

Set Up:
Two people (or more) are stationed initially about 15 or 20 feet apart. 

As the puppy learns the game, you will gradually back up, so that you are further and further apart, and the puppy has to work harder,

physically,( running from the front of the house to the backyard, or running upstairs then downstairs...) and work harder
mentally, figuring out where the person has gone, and working to succeed at Come...

Kids do well at this game, but, to begin with, have them be "team members" with an adult, so they can be supervised, coached, protected.

Each person has some of the puppy's kibble in his/her hand.  This is how the puppy will earn at least part of his breakfast or dinner  for now. (Note:  If doing this with children, the adult can hold most of the kibble, handing over a piece or two at a time, to prevent all the kibble being spilled, and to prevent the puppy from rehearsing "mugging" the child, rather than sitting for them...).  Or, each child can be stationed near a table or bar, so that the kibble can be on the table, rather than in their hands...)

Remind the children to offer the food on a flat hand, "like a plate" and when rewarding, to hold the hand at the puppy's chin, so the puppy does not have to jump for the treat.  Alternatively, they can simply toss the treat to the floor.

The Game:
First person says loudly and cheerfully, "Puppy, Come!"  then backs up 3 steps.  (Moving away encourages the puppy to come, while moving towards him encourages him to go...)
As Puppy gets with 3 feet, say "Sit!", and lift your right hand, palm up, towards your right shoulder.  That is the Sit Signal. 
Say "Sit!" just once, then wait for compliance. 
Hand over the kibble, ("hand flat--like a plate") then ignore the puppy.  ("Be a Tree"= Ignore= Hands crossed on chest, fingers under armpits, eyes to the sky, turn back to puppy. )
Second person says loudly and cheerfully, "Puppy, Come!"  then backs up 3 steps.
As Puppy gets with 3 feet, say "Sit!", and lift your right hand, palm up, towards your right shoulder....etc.
First person calls again, and back up further, so that the two players are getting farther apart, and the puppy has to work harder...