If you get three of a kind of the special cards, that’s when the action happens. If it’s a regular card (like a Logger Dogger or a Barky Sharky) you just place the set in front of you (they’re worth a point) and keep going. You’re hoping to get three cards of a kind in your hand. It’s kind of like Spoons, if you’ve played that. So your draw pile is fueled by another player’s discards, and your discards fuel another person’s draw pile.
You take from your draw pile on the right, and discard into the draw pile of the person to your left. No matter what, you can only have up to 5 cards in your hand. Everyone begins with 15 cards: 5 in hand, and 10 in a personal draw pile.