First things first: I assume this is urgent because it's on a live site. After fixing this, it would be a good idea to set up a dev/test site, so you can try things like this, and play around without breaking the live site ;). Also, start some backups from now (before doing the below).
It depends somewhat on what type the extension the extension is, but you can generally remove a Joomla extension by just removing its files. Even if it leaves remnants in the database, those generally won't actually run.
- If it's a plugin, those files are in
/plugins/PLUGINGROUP/PLUGINNAME
, and maybe /language/LANG/
- If it's a component, those files are in
/components/COMPONENTNAME
, /administrator/components/COMPONENTNAME
, and maybe /language/LANG/
- If it's a module, those files are in
/modules/MODULENAME
, and maybe /language/LANG/
However, if the extension is question modifies core Joomla files (it shouldn't, and this is bad practice, but several do...) then all bets are off. You'll either have to go through the install script and analyze what it does on install, or you'll have to rebuild your Joomla site (might be doable by uploading core Joomla over the top).
Moral of the story: test first, then put changes live!