I would suggest using a tool called Gimp. Gimp is the open source version of photo shop and can accomplish exactly what you want. I think this would be the easiest and most efficient tool. You definitely need to be introduced to Gimp, it will help you in many ways.
OPTION 2 (due to the comment)
This works for Word 2010. Let me know if you need one for a previous version.
- Open Word
- Double click on the picture (This brings up the Picture Tools menu across the top ribbon)
- Click on the down arrow button to the right of "Color."
- Click on the button "Set Transparent Color"
- Click on the color of the picture that you would like to be transparent.