Pets, when hungry, are looking for a specific type of food that they want to eat. The food that they want will be displayed as an icon over their head. You may need to cook, burn, or simply gather the food that your pet wants to eat.
After you collect the food that your pet wants, equip it in your primary equipment slot then stand near them. Tap and hold on to your Scout, drag away from where your pet is standing, then release to throw the food towards them. Your pet will pick it up then eat it. Alternatively, you can tap on your pet and then select the "Feed" option to give them the food.
Once your pet has been fed, you'll see a heart icon over their head signifying that you can receive a reward from them. Tap on your pet then select the "Harvest" option to receive the rewards.
Feeding your pets will also enable them to grow. The more you feed them, the more they'll grow. They will go from Young, Adult, then lastly Mature.