The Puppy Pals Hobby Event is a 7 day Limited Time event which is unlocked after you have completed A Puppy Odyssey.
You can start the hobby buy purchasing a Puppy Play Mat from the Promotions R Us Store. You'll also need a Puppy! If you don't have one you can adopt one from the Pet Store.
Visit the store with the person that you want to participate in the Hobby and adopt one from the selection. You can then place your puppy play mat in the house of your Sim with the puppy (not in another house - as puppy's can't leave the house), and get started with this seven day limited time Event.
What you get: On completion you will unlocked Pet themed clothes for your Sims and you can also unlock the Poodle if you do it within the time period.
These Hobby Events are all generally quite simple. You just need to complete a collection or number of collections to unlock stuff. The difficulty of it is usually determined by the time options you have for the task. Luckily, at the time of writing anyway, there is one option for 1 hour 15 mins. So as long as you are around and playing the game, this is probably the best option to pick to get the most Items for the collection.