There are two different ways to do this in Firefox with no addons or weird configs:
Open Preferences->Search->One-click Search Engines, make sure google is checked, double-click "google" in the keyword column, change it to just "g".
If you want to keep the old "google" term or outright disable Google as a built-in search engine you can still add "g" as a keyword search. Go to Google, right click the search box, select "Add a Keyword for this Search..." and select "g" as your keyword. This works for search forms on most sites that aren't doing insane stuff with javascript or mandating a security token and it generally remembers other form settings as well.