Registering a user account with Zotero allows you to sync your library between multiple computers. To create an account, fill out the form here. You'll need to confirm your email address after submission.
Log into Zotero Standalone and Sync
First, open Zotero Standalone.
In the top left, click Edit > Settings.
In the window that opens, click the Sync tab.
Enter your username and password, and click OK.
Sync your Zotero library (including attached PDF files), by clicking the circle of arrows to the top right.
Now Zotero Standalone will save your library on any computer. Just make sure you've logged in.