Zotero is not a website, but lives on your computer, connected to your web browser. If your hard drive dies, you could lose all of the material collected in your Zotero Library if you don't back up your data!
Create a free account at zotero.org. Then enter the same credentials in your local Zotero Library. You can watch this process in the Zotero 2 video.
Select: 
> Preferences > Sync
Zotero will then automatically sync your local Library with your online account. There is no limit to the number of citations that can be synced, but there is a cap on the free file storage (attached pdf's). If you need to share pdf's with a research group or need access to pdf's from multiple computers, you can purchase more storage.
Syncing is the preferred backup method because it will automatically protect your data. But, there are other benefits to syncing with zotero.org -- it allows you to:
Backup by exporting your Library periodically. Then save the resulting folder to an external hard drive, a web-based system like Dropbox, or wherever you backup your other files.
Select: > Export Library...
(check the boxes to include Notes and Files)
