To install tModLoader, simply run the tModLoaderInstaller.jar file. Java 1.7 or higher is required for the installer to run. The installer will make a window pop up, informing you of either success or failure.

If the installer for some reason does not work, or if you do not want to install/upgrade Java, you may also do a manual install. Go to your Terraria's Steam folder; for most people, this will be "C:\Program Files (x86)\Steam\SteamApps\common\Terraria". Then, copy all these files into that folder. You may wish to back-up your vanilla Terraria.exe first.