Make sure you have created a Zotero account and log in by going to Edit > Preferences > Syncing and entering the username and password you created. Once you're logged in, syncing occurs automatically, but you can manually sync at any time by clicking green curved arrow icon in the upper right to save your library of resources to Zotero's cloud storage. This allows you to access this library of resources from multiple computers.
It is also possible to use Zotero saving only to your local hard drive but backing up your work is recommended.
You can organize sources in Zotero into collections and sub-collections. ("Collections" in Zotero are like folders in other organization systems.) Creating collections for specific courses, topics, or assignments can be very helpful. A single source may be placed in more than one collection.
You can create collections by using the New Collection icon or by right clicking on My Library or a folder to create a new collection or subcollection under it.
Creating at least one collection at the beginning is helpful, because whatever collection you have selected in Zotero will be the default location when you save sources. (The Zotero application must be open to save sources in your Web browser.)