You can download an evaluation copy of Paint Shop Pro from
http://www.jasc.com/ It's a fairly inexpensive program. 

Start by downloading some graph paper. 

The images shown in this tutorial are cropped for faster loading.

Open up Paint Shop Pro, and open the graph paper, 
then go to Window/Duplicate, and close the original image so you
can use it again later.

Then go to Colors/Increase Color Depth, 16 million colors.

Okay! Now your ready to start graphing! 

This is the magic wand tool, it will select the beads you want to color.
Hold down the shift key and individually select the beads you want 
to color in. You will see a little line of "marching ants" around the 
beads you selected. 

Click on flood bucket then on the colors, choose the color you want,

then click
in any of the selected beads. 

Repeat to fill in your design adding each color one at a time.

To save the image, go back to colors and decrease the colors to either 256 colors 
or 16 colors depending on how many you used, gif patterns are generally clearer
then jpgs, less "noise" in them. Then go to file, save as, and in the save window you 
are given a drop down menu, choose gif from that menu.