how do I delete the list of previous searches that pops up when I
click over the search querey window in Google?

One person's feature is another person's bug, huh?  I am assuming you
are using Internet Explorer.  If not, please clarify.

There are two steps:

First, on your menu bar, click TOOLS, then INTERNET OPTIONS then in
the section that says "Temporary Internet Files", press the DELETE
button. Then click the button labled "Clear History"

To delete individual words that come up in the Google search term, you
can simply press down until it is highlighted, then hit "Delete" or
"DEL" key on your keyboard.  To turn this option off entirely, go back
to TOOLS, INTERNET OPTIONS, then ADVANCED.  Then scroll down to the
line that says "Use inline
Autocomplete".  This should be beneath a heading that says "Underline
Links".  This will make it so that future search terms won't be saved.

Thanks for your question and if you need any clarification, please let
me know!

Regards,

-THV

Search Strategy:
Personal knowledge

THE INSTRUCTION TO USE THE EXPLORER TOOLS/INTERNET OPTIONS/CLEAR
HISTORY DID NOT WORK, BUT HIGHLIGHTING THEN DELETING EACH LINE DID,
THANKS
DAVID

On my IE (6.0):
TOOLS->INTERNET OPTIONS
CONTENT tab(up top)->AUTO COMPLETE->CLEAR FORMS
ALTER OPTIONS IF DESIRED->PRESS OK
No need to empty internet cache or history with this method.

"On my IE (6.0): 
TOOLS->INTERNET OPTIONS 
CONTENT tab(up top)->AUTO COMPLETE->CLEAR FORMS 
ALTER OPTIONS IF DESIRED->PRESS OK"

Anonytmouse-ga's answer is the correct one.  It clears online forms
which is what pops up with previous search terms.  To stop this from
happening in the future

1. Click "Tools"
2. Select "Internet Options..."
3. Select the "Content" tab
4. Click the "Autocomplete" button
5. In the "Use Autocomplete for" section, uncheck "Web addresses" and
"Forms."

Search strategy: 8 years of experience in desktop support

--cascadefx

***Clearing previous searches from the Google Toolbar dropdown list***

To clear the list of previous Google searches from the Google toolbar
dropdown list, click on the "Google" button/menu on the toolbar just
to the left of the search box and select "Clear Search History."

That's it.