I am not much of a programmer myself, but one way I contribute is to read through the issue queues of contributed modules that I have experience with. In the issue queues, there are many support requests from inexperienced Drupal users that I am able to answer, even without programming knowledge. I would imagine that the module maintainers appreciate this, because I bet that they would rather spend their time improving their modules than answering basic questions from new users.
Also, in the issue queues, one often finds multiple bug reports on the same issue. Closing duplicates and writing summaries for issue threads that have grown extremely long can help bugs get solved even if you yourself do not have the programming skills to fix them. Further, this gives one great insight into what a helpful bug report is (and how not to write a bug report!)
To get started, check out the guide for how to use the issue queues.