Fortunately, deleting your past searches is easily done. To understand, let's first cover how to access the past searches or search history list, using Google as an example.
Assuming you've got Internet Explorer's AutoComplete on and have searched at Google before, you should be able to click once in the Google search box and get a "drop down" box to appear, listing all the things you've searched for in the past at Google. (Alternatively, you can start typing a query, and you'll be shown any queries that contain the first letters that you've typed.)
Now let's say in the drop down list of past searches is a particular query that you want to remove. Use the arrow keys on your computer keyboard to highlight the particular entry. Alternatively, highlight the entry using your mouse but don't click on it! Next, once the entry has been highlighted, push the "Delete" button on your computer keyword. The entry should disappear.
There's also a method to remove all your past searches, in one go. Of course, if you do this, you'll also delete any other form-based information that Internet Explorer may have saved.
To do this, in Internet Explorer 5 or higher, select "Tools" from the menu, then "Internet Options" and then choose the "Content" tab. Next, look for the button at the bottom that says "AutoComplete." Click on the button which will make the AutoComplete Settings window appear. In it, click on the "Clear Forms" button to delete all your stored form entries.
By the way, I personally find AutoComplete very handy for dealing with all the forms I encounter on the web. If you aren't using it and want it, follow the steps above to get the AutoComplete Settings window. Then, checked the boxes under "Use AutoComplete For" to start having information saved.
Finally, if you are a Google Toolbar user, the techniques above won't work to remove your past searches from the toolbar. Instead, you'll need to click on the Google logo next to the Google Toolbar's search box, then choose "Clear Search History" from the drop-down box that appears