You need to enable your Quest Tracker in your worldserver.conf file by setting:
Quests.EnableQuestTracker = 1
To install the web interface, go in your web server folder and type:
git clone https://github.com/ShinDarth/TC-Quest-Tracker.git
then open the TC-Quest-Tracker folder, copy the file config.php.dist, rename the copy to config.php and edit it properly (it's quite commented).
The TrinityCore Quest Tracker is open-sourced software licensed under the GNU AGPL license.