GIMP
GNU
Image
Manipulation
Program
This is a free program that offers many tutorials acrossed the net to design and create your own logos, banners, animations to your website. There is no trial or monthly fee once downloading it is yours to own.
www.gimp.org
For windows Installation.
http://gimp-win.sourceforge.net/
If you have any questions regarding GIMP this is the best "How to do this" page.
http://en.wikipedia.org/wiki/GIMP
Free tutorials being discussed in this forum, I've learned so much just from reading a few here and there.
http://www.pixel2life.com/tutorials/Gimp/All/