Choose a colour that isn't already part of the image you wish to make transparent. I find a light green works well for most transparencies. Set both the Forground and Background to that colour.

Step 2:

Use the Flood Fill tool to fill in all the areas that you do not want. Play with the Tolerance value, a higher value will fill in a larger area. Zoom in to get the tiny spots that get missed.

Step 2:

Under the Colors Menu choose "Set Palette Transparency" and when asked check "Set transparency value to the current background color". Remember that the background colour in the colour palette should be set to the same colour you used to Flood Fill the image with.
PSP4 users can set the transparency when saving the image. When you choose "Save As..." make sure your doing it as a GIF. Click on options and check "Set transparency value to the current background color".

IMPORTANT: When saving the image click on options and be sure Version 89a is checked.

When your done you should have a transparent image like this one.