Firefox only blocks vulnerable versions of Java so the thing to do is to update to latest version. Unfortunately, simply installing a new version of Java doesn't necessarily remove older Java versions from your computer which will leave you vulnerable. So you'll have to uninstall any old versions of Java before going ahead with the update.

Go to the Java download page and download the latest Java installer but don't run it yet.
At the top of the Firefox window, click on the Firefox button (File menu in Windows XP) and then click Exit
From the Start Menu in the Windows taskbar, select Control Panel. The Control Panel opens.

Open the Windows program listing.
(Windows Vista/7) Click Programs and then Programs and Features.
(Windows XP) Double-click Add or Remove Programs.
From the list of currently installed programs, select any Java or Java Runtime programs.
To begin the uninstall:
(Windows Vista/7) Click Uninstall at the top of the window.
(Windows XP) Click Remove on the right of the Java listing.

Note: Complete the uninstall process before proceeding.

Run the installer you downloaded in step 1.
Start Firefox

Java should now work as expected.

If you had previously selected Disable in the blocking dialog, you may need to enable Java again:

At the top of the Firefox window, click on the Firefox button (Tools menu in Windows XP), and then click Add-ons. The Add-ons Manager tab will open.
In the Add-ons Manager tab, select the Plugins panel.
Find the Java Platform or Java Runtime item and click Enable.