How do I change the green sidebox buttons?

How do I change the green sidebox buttons....like the categories, sponsors, to an image that i created?

Do you mean the sidebox headings? For those, the easiest will be to install Image Titles from Free Addons. Then save the images with the correct filenames, and they will automatically be used in place of the standard text.

If you mean just the heading backgrounds, those are created in the Classic template by a background-image called tile_back.gif. You can make your own version and replace it.
If you need more help, post a link so we can see exactly what you have and what you want.

so I can just replace the tile_back.gif graphic with my own jpeg file...and that should do it?

No, then youi'll have to change all mentions in the stylesheet of tile_back.gif to yourimagename.jpg.

Or delete the original tile_back.gif and replace it with your own file (in gif form) named tile_back.gif.

The point being made here is that if you call your image abcde.jpg, then all references to it in the code (including CSS code) must be jpg too.

Right now, the stylesheet calls it tile_back.gif

... and while it is perfectly OK to use jpg images, you need to make sure that the filename AND extension are consistent throughout the site.