Reporting bugs would be the main thing.

The amount a non-coder can contribute back is rather limited I think. If I make use of code or designs from another GPL product I always try to contribute back something, even if it is just a coding tip or similar. Most themers and plugin developers really appreciate that, just a simple tip on how to improve what they're doing can be quite useful. I've had the same thing happen too, users have sent in code snippets demonstrating how to improve my software, it's very useful and much appreciated.

From my own personal experience as a plugin/theme developer, I think the best thing a non-coder can do to help with bug reports, is to make sure you report the exact problem you are having. If you can't explain it, provide an image. An image paints a thousand words. Having said though, make sure you include a link as well if it something which is specific to your site (or a plugin you are using). I receive lots of reports on "bugs" which people think are in my software, but they fail to provide a link back to their site so there is literally nothing I can do to help them or to fix the problem. Usually what they're reporting is a problem with their own coding, but I can't let them know that usually because they don't provide enough information for me to figure it out. All the time I waste trying to work out problems due to lack of information can be quite horrendous and it would make my life a lot easier if more thorough reports were given.