For Paint?
Take the eyedropper and hold [CTRL] while picking a color. This will transfer the color to the box behind the left-click and right-click cells in the bottom-left, and that is the .GIF's transparency color. Anything that is that color within the graphic is transparent.
And yea, make sure you save it as a .GIF when you're done.
(However, for this particular forum, it's probably better to get a more advanced image editor and give it true checker-transparency since backgrounds here swap with every other post)