The most reliable way to move your entire library to another machine is to copy the Zotero data folder from your first machine to your new machine.
Be sure to close Zotero 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.
You can also automatically sync your library between multiple computers via the Zotero servers.
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, and this will break connections with any existing word processor documents.