This online site often works for me:
http://www.online-image-editor.com/ If your image isn't already in the .png format, check the box to convert it to .png during upload. Then go to Wizards/Transparency and click on the background colour to render it transparent. Save, again as .png.
This isn't foolproof, it works best when the background is monochrome and the background colour isn't also present in the image itself (in which case you may get transparent spots here and there in the figure, where you don't want them). But it's worth a try - when it does work it works very well, and with time you'll learn to predict which images will work and which ones won't.