There is an easy way to export your entire library and take it with you.
On your computer, open the Zotero preferences, choose the Export tab, select the items, and drag them on a Word file that you will then save to your USB drive.
Manually importing a Zotero library from one computer to another is not recommended. The most reliable way to do so is to copy the Zotero data folder from your first machine to your new machine.
The easiest way to export/import your library is to automatically sync the library between multiple computers via the Zotero servers.
If you're regularly using more than one computer in your research, Zotero's sync feature can keep your library up to date on all of them. Zotero can store a copy of your library on the Zotero.org server and check it for updates whenever you open your library on a different computer. All your computers must be running the same version of Zotero.
First, set up a (free, of course) Zotero.org user account. Then:
Repeat this configuration on each of your computers. Any updates you make on one of your computers will be reflected on the others. This even works to synchronize your library among Windows, Mac and Linux computers.
For more details and help troubleshooting sync problems, check the Zotero site.