Although this method isn't exactly "new" out there, I wanted to share this because I have never seen my shoes looking this nice, and I was so impressed by the outcome that I thought you may want to try it out too. I also don't like getting the entire shoe wet so this way worked out well for me. I picked up a few tips from Melissa at Clean My Space and altered them a bit, and used them on a wider range of shoe surfaces.
If you're looking for squeaky clean shoes, then this may not be the DIY for you. It gets a lot of stains out, but if you never clean your shoes like me and have stains from things other than dirt, the solution used below won't be able to get out everything.