Once you have downloaded the Zotero software, it's a good idea to create a Zotero account so you can save and sync your citations online, as well as on your own computer.
To create an account:
Go to the Zotero website and click "Log In" in the upper right corner.
Then, choose Register for a free account.
After you have registered, open the Zotero software on your computer and click on Edit--Preferences--Sync
Enter the username and password that you just registered in the Zotero website and click the "Set Up Syncing" button.