We all have faced this problem in our early days, let jump straight into business shall we.
Download GIMP free here: http://www.gimp.org/downloads/
It’s the most powerful free image editor on the planet, so try to learn to use it and you’ll love it like me.
Watch this short video to learn how to make the background of an image transparent:
Please keep in mind that not every image format supports transparency, so the format I recommend to use in PNG(if you watched the video you’ll notice I mention this).