Hi Bryan,
You'll need to use the Gemini work-item tracking system located at support.dotnetnuke.com to log work items. Once you create an account, you'll have access to the public DNN project areas. The workflow system used here involves a DNN team member (usually Alex) validating the issue, after which it is moved to the "main" project for further review by the core team. In my experience, I have found them very responsive to issues submitted in this manner, with the likelihood of incorporation being greatly increased with detailed code corrections.
This is the extent of public interaction with the DNN source. Non-core members are limited to posting their suggested code modifications within the work item for the core team to review. As far as I am aware, there is no publicly-accessible checkout/checkin process available.
I'll leave it to those with more authority to suggest other ways in which a person might become more involved with the DNN project.
Brandon