Once you have download the file, either a .Zip or a .RAR archive you will need a tool like 7Zip or WinRAR to unpack it in your X3 Terran Conflict game folder. If you don't know where it is located, it's usually in Program Files/Egosoft/X3TC. If you are using Steam for X3, it's somewhere in the Steam installation folder. Overwrite existing files if needed.
Start X3 and load your savegame (or start a new game). If you're installing a script (like Anarkis Defense System) you should receive a confirmation message. If you have installed a plugin (like Pirate Guild), you will need to go to your Artificial Life menu ( [Esc] / Gameplay / Artificial Life ). Look for the line relevant to the plugin you've just installed. Enable it. You will receive a confirmation window telling you everything is Ok.
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Except if specified otherwise in the release notes you'll just need to unzip the new version over the previous one, and when a game is loaded the plugin will upgrade itself. Sometimes scripts using hotkeys will reset their shortcut during upgrade.
For some scripts and plugins it may help to enable the script editor first. To do so, please follow the next few steps: