Zotero saves all of the information in your library on your local hard drive. For more info on this, see the next page "Zotero Data - On Your Computer". This is fine if you only use one device to access Zotero and/or do not want your Zotero data stored on US servers.
Most people choose to use the free cloud storage on Zotero's servers. This creates an always-up-to-date backup of your data. You can also sync your devices with the Zotero Cloud storage so that you will always be seeing the latest version of the data, no matter which computer or device you are using. It also allows you to create group libraries which can be shared with collaborators.
The following video walks you through the steps to set up your Zotero cloud storage. You can also see screenshots of the steps below.
Covers how to make a Zotero account, sync your library so you can access it from any device, and create a group for collaborating with others. (3:37)
To activate Zotero's cloud storage, you need to set up a Zotero account. If you have not already set up an account, go to the Zotero website, and clicking Log In in the upper right corner of the page.

To learn more about setting up a Zotero account, see the Create a Zotero Account page.
To use Zotero's cloud storage, sync your Zotero library to your Zotero account. Select the sync icon in the upper right corner of your Zotero library then open Sync preferences.

Next enter your Zotero username and password to connect to your cloud storage space.

Now you can use Zotero on multiple computers, create Zotero Group libraries, and use Zotero's cloud storage to back up your data.
You can choose which data gets backed up in the Zotero Preferences settings. There are two kinds of data that Zotero can sync. You will probably want to sync them both.
