Zotero Documentation recommends this method as "the best" way to use Zotero on multiple computers.
If you will be using only computers that have Zotero installed (e.g., your home computer and your office computer and a laptop, or your laptop and the computers in the Information Commons in Ellis Library).
This method requires you to set up a free account on zotero.org.
Zotero's online syncing allows you to access your Zotero library on any computer with internet access and Zotero installed. Zotero syncing has two parts: data syncing and file syncing. For file syncing, you can use either Zotero's data storage, or another WebDAV option such as
Data syncing merges library items, notes, links, tags, etc.—everything except attachment files—between your local computer and the Zotero servers. It also allows you to view your library online on zotero.org. Data syncing is free, has no storage limit, and can be used without file syncing.
Zotero File Storage is the recommended file sync option and has several advantages over WebDAV syncing, including syncing of files in group libraries, web-based access to single-file attachments such as PDFs, easier setup, guaranteed compatibility, and improved upload performance for certain files. Each Zotero user is given 100 MB of free Zotero File Storage for attached files, with larger storage plans available for purchase.
For full instructions and more information on how to sync your library across computers, see Zotero's Syncing page.
If you use Zotero only on your own computers, you can simply copy your Zotero data directory to the portable drive and set Zotero on each computer to use the same custom data directory on the drive. You can set a custom data directory in the Advanced tab of the Zotero preferences.
If you do your online research on multiple computers, including MU lab computers that do not have Zotero installed, your best option is to run a copy of Firefox directly from a portable drive, which gives you access to your Firefox settings, such as bookmarks and history, in addition to your Zotero data. Instead of using the browser installed on your lab computers, you will use the browser installed on your flash drive - Portable Firefox - on which you have installed Zotero. See Portable Firefox for more information.