Last updated February 28, 2013.
Every project features a tab with Git instructions on the Version control tab (as shown below). On this tab either as a regular user or project maintainer you can find instructions for accessing the git repo for a project.

For project maintainers
The Git URL provided to you uses ssh to communicate with the drupal.org servers. You can only push changes to your project's repository using ssh.
N.B. Git submodules, while allowed by the repositories on drupal.org, will not be included in releases.

You can also switch to the view available to non maintainers (e.g. if you want to see the right instructions to provide other people). That view is shown in the section below.
For users who are not committers
The tab is also available, but shows a http URL for cloning the project Git repo. You cannot push useing this URL.

Comments
Local/Remote branches
I ran into this trying to setup a local branch tied to a remote branch.
I tried
git checkout -b local remotes/origin/7.x-1.xand then could only push changes I committed to local bygit push origin local:7.x-1.x.rfay advised me to look up tracking branches:
git checkout --track origin/7.x-1.xAnd then it should work according to the above instructions.
You can also clone the
You can also clone the repository completely and let GIT create local branches for all tracking branches for you. See GIT documentation for more info (or send me a message and I will look it up and post it here)