Watch Me is one of those basic commands that comes in very handy all through your dog's life. It is a universal command, necessary for pets and show dogs alike. As a matter of fact, I do believe it is a critical component of show dog training.
Just like getting your dog's attention by saying his name, the Watch Me is used to get and keep his attention. A strong Watch Me in a pet pup can be a precursor to lots of things, not the least of which is a competition-ready Heel.
To begin teaching a Watch Me, simply take a treat between thumb and first finger. Start with the right right at the tip of your dog's nose and draw it towards your own nose. As soon as the dog makes eye contact (or appears to, as he is probably actually watching the treat), click and / or say "Yes!" Then give him the treat. Repeat this several times, until he will unfailingly follow the treat and make eye contact. Then it's time to go ahead and add in your word command.
As you draw the treat from his nose to yours, say ONCE, "Watch Me" then click and treat the eye contact. As he gets the idea, start phasing out the treat by leaving it in your other hand and drawing his attention with just your fingers. Start with leaving out the treat every other time, then treating only every third time, fourth, fifth, etc. Once you start getting more times without the treat than with, it's important to randomize your treating so he does not begin to expect a pattern to when there will be actual tricks involved. If he does expect, he may only work on those times when he expects a treat.
To lengthen and strengthen your Watch Me, very simply hold the contact longer before you click and reward. If you start with barest eye contact, work up to 2 seconds, then click and treat. Then 5 seconds, then 10, and so forth, until you can hold that contact indefinitely.
And that's all it takes. As the command strengnthens, then you can start throwing in distance and distractions. Rather than sit the dog in front of you, ask for a Watch Me from a foot or two away. Then from 4 feet, then when he's busy sniffing or gazing into the distance. Work up to being able to interrupt any activity and get a strong Watch Me that lasts until you either change the command (Watch Me! Down!) Or release (All Done!)