Remove or disable java due to the security issue

For Firefox,
Open Tools/Add-ons/Plugins (Keyboard shortcut is Shift+Ctrl+A) and find it on the list. Click the 'Disable' button to the right of it to disable the plugin. (Note that I've never bothered installing it so it's not present in my screenshot. If you have it installed you will see it here.)

FF plugins

For Chrome,
Go to chrome://plugins/. Find it in the list of plugins and click on 'Disable'. (Once again I am using Flash in my screenshot example because I never installed Java.)

Chrome plugins dialog

Note that the Java plugin and Javascript are two different things. See here [Java.com] or here [stackoverflow.com] for an explanation of the differences.