First, make sure Zotero is installed by looking for the Zotero menu option in Firefox's Tools menu. Make sure that you have the most recent version of Zotero and an up to date version of Firefox.

If Zotero appears in the Tools menu, make sure the status bar itself is visible: under the View menu, ensure that Add-on Bar (or Status Bar in Firefox 3.x) is checked. You should also be able to open the Zotero pane by selecting Zotero from the Tools menu.

If you don't see Zotero in the Tools menu, go to Tools→Add-ons→Extensions and look for Zotero in the list. If Zotero doesn't appear, install it from zotero.org. Also make sure you have the latest version available.

If Zotero is listed in Tools→Add-ons→Extensions but doesn't show up in the Tools menu, you see the message “This add-on will be installed when Firefox is restarted” even after restarting, and/or you get other errors during installation, try the steps under Corrupt extension files on the Mozilla add-ons troubleshooting page.

You should also try disabling all other Firefox extensions, as some are known to cause problems with Zotero.