Why do you need a GitHub username?
As Dreamwidth is a free/open-source project, we need somewhere to put the source code so that other people (you!) can work with it. We've chosen to use GitHub for this, in line with most current projects like ours.
As we use GitHub's issue tracker for submitting changes to the source code, we've found that it's easiest for everybody if developers wanting to make changes to the code have a GitHub account, and have the two main repositories - dw-free and dw-nonfree - "forked". (Forking a repository on GitHub means that you have your own copy of the code to work with.)
Forking the two repositories is easy. First, sign up for a free GitHub account (if you don't already have one). Then, follow each of the two repository links in the previous paragraph and, for each one, click the "Fork" button in the header at the top right, next to the "Watch" (or "Unwatch") and "Star" buttons:
After doing this for both dw-free and dw-nonfree, you will have your own copy of the code and can apply for a Dreamhack by using the application form. As part of the Dreamhack setup process, we'll download your copy of the code and set it up in your own area, so that you can work on the code safely.
That's pretty much it! If you're ready to continue and have a GitHub account with both repositories forked, you can move on to the application form. If you still need help, go ahead and submit an application anyway; I'll get in touch and answer any questions you may have or help you with whatever you need.