Last updated June 23, 2015.
One of the best ways for contributing is by helping the module and theme maintainers to keep their issue queues clean. It's a good way to get familiar with a module before you use it.
There are several ways you can help maintainers.
Help out with support requests
Often, questions are asked in issue queues that are either very basic, or are something you might have encountered before by using the project. You can answer such questions and close these issues.
If you find support requests for Drupal core, you may also fix the issue by redirecting the poster to other support channels, using the template in templates for issue status transitions.
Mark duplicate issues as duplicate
Many issue queues have duplicate issues. If you encounter one you should find the oldest of the issues and mark the others "duplicate" with a pointer to the original, unless a newer one has a patch and lots of activity around it.
When you mark one issue as duplicate of another, it's helpful to indicate the relationship in both places. Add a comment to the duplicate issue that says something like "Marking as duplicate of [#xxxxxx]", but also add a comment to the main issue, something like, "Marked [#yyyyyy] as duplicate of this issue." That helps maintainers see when a particular issue has a lot of requests around it, and also provides an easy way to find other information that might help resolve the issue.
Confirm whether bug reports are still valid
If you can not reproduce a bug, mark it as "closed." If you can reproduce it, confirm that you see the issue too, preferably with more details on how it can be reproduced or where you think the problem might be.
Ask for more information on unclear requests
If it's not obvious what's being asked for, mark the issue to "postponed (maintainer needs more info)" or try and fill out details yourself.