If you create a Zotero account, you will be able to access your reference library from anywhere. Simply go to the Zotero Register page and follow the instructions.
Once you create your Zotero account, you will want to sync your data. Data syncing will merge your library items (i.e. references, notes, links, tags) between your computer and the Zotero servers. To start data syncing, open Zotero and click on either Set up syncing from the Welcome page or Preferences from the Edit dropdown menu.
You will then need to enter the username and password that you just created and click on Set Up Syncing.
Make sure the Sync automatically box is checked and click OK.
If you attach any files to your reference library, you will also want to set-up file syncing. This will allow you to view and share attached PDF's, images, audio and video files between your computer and the Zotero servers. Zotero gives you 300MB free storage space for attachments. If you need more space, you may purchase a storage subscription directly from Zotero. To start file syncing, go to Preferences from the Edit dropdown menu.
In the Sync menu, make sure the Sync attachment files in My Library using Zotero box is checked. You can choose whether to download files at sync time or as needed.