Or just click the big red button on that page...click the "allow" bar that pops up at the top of Firefox....then wait 4 seconds to click "install". Finally you have to restart Firefox.
Are you having trouble because you are in a different browser? Chances are, if you can't figure out how to install firebug, it probably won't be of much use to you. For everyone else, it's wonderful.
now a days, a new 3.6.3 under the FF, when you install firebug 1.5.3 always prompts a download error 278, tried several issues remain, and later on directly from third-party sites to install the next one, done!.
sometimes the latest Firebug is not tested with the latest Firefox browser update, probably wait a while to get things sorted .. else you can use IE -> Internet Developer Toolbar (should comes with IE 8, else has to download separate for IE 7) for temporary usage.