Quizlet is available in the Chrome Store as a free app and can be added to all Chromebooks/Google Apps for EDU student accounts through a Google Apps Admin Panel.
Your students will be able to launch Quizlet just by clicking on the icon when they login to Chrome.
You'll need to check whether you have Admin access to Google Apps for EDU or ask one of your school admins who does.
Google Apps Admin
Once you've logged into your admin panel for Google apps for EDU (under google.com/a/ + your domain's name), go to Settings.
And then select Chrome OS .
Choose Applications and select the Organizations whose settings you would like to manage (such as students, adults, etc).
To preinstall Quizlet on your students' accounts, click manage pre-installed apps under Apps and Extensions.
Click on Chrome Web Store and Search for Quizlet and add it.
Save your settings and your students will all see Quizlet as an icon next time they boot up!