When you first join the game, you gotta press that green "Start Game" button.
So you get an option to pick from four different pets (You'll get more options later in the game.) The pink kitty, the orange kitten, the brown puppy or the grey doggy.
Once you've made your pick you should see the view in the picture above.

Right! Now you just spam the "Feed Pollock" link/button until it says "I'm thirsty,
You have to buy Water" Press the word "Water" and buy it. It only costs 5 coins, which you SHOULD have 10 ^^ Buying it is a must~

Just Give Water... Until you can pet it! :0 Repeat until you reach level 5.