Creating a free Zotero account allows you to sync your library to Zotero's cloud service so that you can access it from anywhere. Having a Zotero account is also the only way to have group (shared) libraries.
Once you have created a Zotero account, you will be able to sync your desktop Zotero library and your web library. Syncing your libraries will merge library items, notes, links, tags, etc.
In order to set up syncing, you will need to go to Zotero on your desktop and open Edit > Preferences > Sync. There, under "Data Syncing," you will enter the information for your online Zotero account. You can also choose whether to make syncing automatic or manual.
Under "File Syncing," you can choose to have attachment files (such as PDFs) synced using Zotero's file storage. However, if you are using the free version of Zotero, you only get 300MB of storage. In order to avoid filling up your limited storage in your Zotero web library quickly, you should follow our instructions for managing PDFs with ZotFile. ZotFile allows you to connect items in your Zotero library to PDFs and other files saved with a cloud storage provider. If you use this method, you will not be able to access full-text attachments directly from your web library.
Zotero groups allow you to collaborate with others by having shared group libraries. You can create a group in Zotero by going to the New Library icon located in the top left of the Zotero window. (Hint: it looks like a box with a plus sign.) Then select New Group... from the dropdown. This will automatically open Zotero's "New Group" page in your web browser, and there you can name your group and choose what type of group you want--public, open; public, closed; or private.
You can also create a new group directly from your Zotero web library by clicking on "Groups" at the top of the page and then choosing "Create a New Group" from the Zotero groups page.
If you have enabled syncing between your desktop Zotero library and your web library, the group will now appear in the left sidebar of your desktop library, below your main library. Note that items in your group libraries are not automatically added to "My Library." If you want items from a group library to be in your main library, you will need to add them.