Helping people with computers... one answer at a time.
Sometimes you just want to clear what you've searched for from the browser's history. These steps clear that information in Internet Explorer 7.
The good news is that it's apparently very similar to IE 6.
But naturally the names and locations of some items have changed.
In Internet Explorer 7, hit the Tools menu, Internet Options menu item, and you should see something like this:
Underneath Browsing History, click on Delete and you'll get this:
Obviously there are many things you can delete here. If you're looking specifically to clear the searches that you've entered into the Google home page, then click on Delete Forms...:
Hit Yes and you're done.
Note that this will clear auto-complete entries from all web forms, not just the Google homepage.
And there are still several other places in Windows that remember things for you - I'll refer you to that previous article: How do I delete history items from my Google tool bar? for more of those.