What I'm trying to do is very simple, but I'm having a hard time finding
instructions on tutorials, lessons, websites, etc., so maybe someone out there
can point me in the right direction? Here's exactly what I'm trying to do:
[bullet]When the mouse rolls over a defined button, I want another image to
pop up elsewhere on the stage and then disappear once the mouse rolls
off.[/bullet]
Step by step instructions would be much appreciated. Thanks in advance! =)

There are a few ways to do this. But Ill give you two of the easiest ways I
know.

1) If it doesnt matter how far "nested" the items are (i.e. the other image
you want to show up somewhere else); under the "button" where it shows, mouse
over, hit, etc... keyframes...turn the mouse over instance into a movie clip.
Go inside that movie clip and add a new layer with the image you want to place.

2) You can also do this more elegantly with actionscript. Trying using
tellTarget..

tellTarget("target") {
statement(s);
}

In this, you could define the location of your image you want to place. So all
of it would be ...(under the mouse over section for your button)

on(rollOVer){
tellTarget(yourImage){
statements;
}
}

..Good luck

Thank you! You're the greatest! It works!