Head over to https://git.matrix.ac and you will see a list of repositories stored on the matrix.

To host a public repository place it in ~/public_repo.

You can then add it as a remote, using:

git remote add origin matrix.ac:public_repos/<repo>

And you can clone via SSH:

git clone matrix.ac:public_repos/<repo>

And you can clone via HTTP:

git clone http://git.matrix.ac/<user>/<repo>

Currently there are no groups or finer permission. If this is wanted we can work something out.