Firebug is not officially compatible with Firefox 6 since as of this writing, Firefox 6 is on early alphas. However, forcing compatibility works with it. For that, just install Nightly Tester Tools addon and in Tools>Nightly Tester Tools, check “Force Addon Compatibility” and restart Firefox. Now, you will be able to install and use Firebug.
[HOWTO] Firebug on Firefox 6
