How to download a Linux version of Terraria on Steam
Solution 1:
Install the Steam client for linux that best suits your distribution (latest version found here) and make sure it has all prerequisites to run.
Start the steam client as your regular desktop user and sign in to steam using your steam credentials.
If the game you want to play is supported by steam under SteamOS/Linux, it should be marked as such in your library and you'll be able to install it the usual way. (Terraria is marked as such so you should be good.)
Enjoy your game.