The first thing you will need to do is render the image (take the white background out) - using either the fuzzy select tool,

or the scissors tool -
Take your time and do it nice and neatly. Make sure to add an alpha channel before you start so it will delete the white area in the back ground. After you get your image cut out - you can then just resize it, and move it where you want it and save the image as a PNG.
Save your image as a PNG (in the save as dialog)
Then just click okay on the dialogs that pop up and you should be fine.
Most are just default settings.
Just make sure that when you do save it - those checkered areas are showing as your background.
PNG will see that as transparency.
If you need more help i will be glad to do this for you.
