Firstly... This is only my way of doing it... there are probably many others... but this works for me!

Here is our starter. Take your image and make sure it only has 1 layer... because what we are actually doing here is removing a piece of an image straight into the emptiness of outerspace... aka the background of a page so that the colour of the page that it's will show through the image.... that made absolutely NO sense... but anyways! Now for mine... I'm removing just random chunks because I have no reason to remove except for this tutorial :) so I'm going to remove more than one chunk at a time... this requires me to open up one of the selection tools (rectangular for me) and where it says "Mode" at the very top, click the second button aka Add. This makes it so you can make several selections and not have your old ones disappear! Ooo! Another handy tip... especially for making icons... Holding down the shift key while making a selection will make the selection a perfect square! yay! Back to the tutorial... I've made my selections...

So now I use my handy dandy Ctrl-K or if you like the oldfashioned way - Image>Edit>Clear - And all your selections will magically disappear! Hurrah!

Which will show up on a page like this...

Save your image as a .gif... or the transparency might not work! Now... There are many other ways to do this... Eraser tool, other selectors will work etc. I also outlined(see Outline Tutorial) the selections in black for a neater look. So Experiment away!