Trick training is one of the training mini-games you'll complete with Stacie. This one is a bit of a grind but quite easy, just train your pup in the tricks by following the button prompts and raising your dog's learning meter through QTE button presses.
You can select this minigame from the training menu, so long as you have a puppy at 100% energy. With this in mind, you can cycle through your puppies once you have a full kennel to grind this out pretty easily (or you can just do it every time you have a puppy at 100%).
UPDATE: I have confirmed that to be able to freely select any of the activities from the grooming or obedience menus in the kennel (essentially anything that is not vaccination, cavities, or flea removal) you need to have at least one puppy in your kennel who is "ready to graduate" (ie you've completed all of its rescue activities) AND they must be charged to 100%. Happy achievement hunting!
