The most reliable way to move your entire library to another machine is to copy the Zotero data folder from your Firefox/Zotero profile on the first machine to the Firefox/Zotero profile on your new machine.
To locate your Zotero data, open the Zotero preferences under the Actions ('gear' icon) menu and click “Show data directory” in the Advanced tab. See here for the default locations of the data folder.
Be sure to close Firefox/Zotero Standalone on both machines before copying the Zotero files.
In addition to the above method, you can also use a USB drive to sync your data between computers. Finally, Windows users can also transfer their entire Firefox profile with the tool MozBackup.
You can also automatically sync your library between multiple computers via the Zotero server. Note that files (attachments such as PDFs, snapshots, etc.) are synced separately from data, via either Zotero File Storage or WebDAV.
Exporting and importing your library (for instance via Zotero RDF) is not a recommended option. None of the available export formats allow for a complete transfer of your library data.