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.
The latest stable version of Firebug is 1.6 which is compatible with Firefox 3.x. If you have Firefox 4 as your default browser, you may be miss this extension. Firebug 1.7 is under development and the latest version available at the time of this writing is 1.7X.0a7. You can install it from Firebug 1.7 releases page. Note that it is still in alpha stage of development and may have several bugs.