Ah well, a bit late, but I finally get back to tricks!
The first trick we taught Mawson was fairly simple and we learnt it during puppy school.
It is the hand shake.
They use that to get me embarrassed in front of my mate in the park.
It's easier if the pup is in the sitting position (luckily Bodhi just explained sit today!). The whole idea at the beginning is to get mister pup to lift his paw to get something that doesn't come easy. They nearly all do that. So, what you need to do is get a trigger in your hand, usually it works best with little bits of food. Show it to the puppy then close your hand, enclosing the food. Any puppy or dog will nose it and try to get to it, and they will certainly fairly quickly get their paw up and paw your hand. When that happens, get the cue reward either yes or click from the clicker and give the treat. Do not say anything else at that point. Repeat the action a few times, trying to make sure that mister pup makes a swift paw action touching your hand once with his paw and then go onto something else. Over the next few days repeat the simple action without saying anything refining the paw action. When it becomes regular, start adding your cue word after the action (it is important to start associating the word with the action but perform the action that the pup is learning first, then reward and add the word).
When that word gets associated, start moving the word earlier and use it as the trigger for the action, and then phase the treat out. Offer your hand as before but without the treat in (keep it in the other hand) and get the action going. Paw to the hand you are offering, big yes, then reward from the other hand.
Mum don't say to phase the treats out, keep the treats going, yes, aaallllll the time, treats treats treats. Actually you don't need to ask anything, just give the treats. Mum can do the trick part, I do the treat part...
The thing with teaching any behaviour is being patient. Just think about when you learnt to tie up your shoelaces. I am sure there was quite a few failed attempts and it took a little while to stick in your brain, even though now you find it (hopefully) trivial. Well that is the same with anything new you teach. If you go a bit too fast and things get a bit pear shaped, do not hesitate to take a step back and go back to the previous step.
The step where there are treats... WHAT mum? Why are you looking at me like that... I'm trying to help...
This has proven really useful for us as Mawson can be a bit shy of people and we have been succeeding to relax him by teaching him to say shake the paw (hand!) of people we meet in the street to good effect. By staying at a little distance he just says hello and gets treats and everybody relaxes.