Images need to be saved as a .gif or .png in order for transparency to show (.png gives slightly higher quality images, so that's usually what I go for). If the image you want to use is already transparent (like my
Lissa sprite, all you need to do is crop and resize and make sure to save the new, edited image as the correct file type. If the image you want to use has a white or coloured background, you'll have to erase the background with image-editing software in addition to the cropping, resizing, saving, etc. In terms of game sprites, etc. it's usually easiest to try and find a version that's already transparent (gogo Spriter's Resource), but obviously not always an option.