If you want IE to be the default, go to Tools->Internet Options->Programs Tab, check the box at the bottom for IE to check that it is the default browser each time it loads. Then run IE and tell it to make itself your default browser.
If you want FireFox to be default, go to Tools->Options->General, check the box for Firefox to check that it is the default browser each time it loads. Then run firefox and tell it to make itself your default browser. Mozilla should be similar to Firefox, if you use another browser I can't help you, but it will probably be similar.
Note that this is a system-wide setting, so it will affect programs other than Outlook (like IM programs)