While you'll have access to more functions and features if you're able to download Zotero to your computer and used it with Microsoft Word, you'll still have access to a lot of functions if you only use Zotero online.
If you're using a Chromebook, Zotero online is how you'll use the tool.
If you're not able to download Zotero to the computer you're using, you can still add to your online library using the Connector:
If you're not able to download Zotero to the computer you're using, you can still add to your online library using the Connector: