If you are going to use more than one computer to work on your research, you will want to synchronize your library. Please note that you must use the same version of Zotero on each computer.
First, you'll need to set up a free Zotero account here.
Next:
Open Zotero preferences (via the gear menu) and select the Sync tab.
Enter your Zotero user name and password.
Check the "sync automatically" and "Sync full text content" boxes
Check both boxes under File Syncing and choose Zotero storage for My Library. This will sync your PDF attachments as well as citations.
Now, click the green circular arrow button at the top right corner of the Zotero window and your library will be uploaded to the server.
Repeat this on each of your computers so that any updates you make on one of your computers will be reflected on the others.