The official public repository is hosted on Github. To get the code, install git and run:
git clone https://github.com/xinu-os/xinu
This will generate the directory "xinu" containing a local copy of the repository. Note that this is a standalone repository that can be used without access to the Github repository. This constitutes a difference from Subversion, which is more centralized.
Git is documented extensively in many locations, for example in the "Pro Git" book. But in one sentence, a very basic workflow is to modify files, use "git add" and "git commit" or "git commit -a" to commit the changes to the repository, then use "git push" to push changes to a remote repository.
Branches in git are fast and easy to use, so please develop experimental features in their own branches. Code pushed to the "master" branch should not be broken.