Once you start the game, you will need to choose between Buck (strong), Nix (balanced) and Molly (agile) to get to action.
When you finish the practice mode and continue battling, you will be able to get the other two Characters you didn't choose initially!
As you progress in the Leagues, you're going to be able to unlock more Zoo friends. You can check which Characters will be available on the next Leagues by tapping your total number of trophies. This will show your progression, so you just have to scroll.
The Characters are always released from inside Crates that you can get as a reward or purchase with Gems in the game store.
Just keep in mind that you are only able to purchase Crates and Toolboxes at your current League. For example: If you are on League 4, you cannot expect to receive the Character Duke, because he will only be available from level 5 on. You can always check the number of the crate league by tapping on it and seeing the number on the left of its name.
And that's it. Go get them all, Zoobster! :)