How to make the cell look different bases on the result of the formula?
There is something in the help for 2003 about it, but that is truly incomprehensible!
For instance, I would like to get the cell to have green background if result is TRUE and red one if result is FALSE. If not the background, the font colour will do.

Incomprehensible?
Simply use Format - Conditional formating and set what you want

In order to get the conditional formatting to work you have to first select the data you wish to format and then choose the conditional formatting button. From the second list choose "Equals to" and type for an example TRUE. From the "Format" button choose the color of your liking. To get the tool to color the "FALSE" cells in a different color, choose the conditional formatting again and do the same procedure all over except next to "Equals to" type FALSE.

Hope this helps.

Rgrds,
Kristiina