First, clone a remote Git repository and cd into it:

$ git clone git://example.com/myproject
$ cd myproject

Next, look at the local branches in your repository:

$ git branch
* master

But there are other branches hiding in your repository! You can see these using the -a flag:

$ git branch -a
* master
  remotes/origin/HEAD
  remotes/origin/master
  remotes/origin/v1.0-stable
  remotes/origin/experimental

If you just want to take a quick peek at an upstream branch, you can check it out directly:

$ git checkout origin/experimental

But if you want to work on that branch, you'll need to create a local tracking branch which is done automatically by:

$ git checkout experimental

and you will see

Branch experimental set up to track remote branch experimental from origin.
Switched to a new branch 'experimental'

Here, "new branch" simply means that the branch is taken from the index and created locally for you. As the previous line tells you, the branch is being set up to track the remote branch, which usually means the origin/branch_name branch.

Now, if you look at your local branches, this is what you'll see:

$ git branch
* experimental
  master

You can actually track more than one remote repository using git remote.

$ git remote add win32 git://example.com/users/joe/myproject-win32-port
$ git branch -a
* master
  remotes/origin/HEAD
  remotes/origin/master
  remotes/origin/v1.0-stable
  remotes/origin/experimental
  remotes/win32/master
  remotes/win32/new-widgets

At this point, things are getting pretty crazy, so run gitk to see what's going on:

$ gitk --all &

How do you create a new project/repository?

A git repository is simply a directory containing a special .git directory.

This is different from "centralised" version-control systems (like subversion), where a "repository" is hosted on a remote server, which you checkout into a "working copy" directory. With git, your working copy is the repository.

Simply run git init in the directory which contains the files you wish to track.

For example,

cd ~/code/project001/
git init

This creates a .git (hidden) folder in the current directory.

To make a new project, run git init with an additional argument (the name of the directory to be created):

git init project002

(This is equivalent to: mkdir project002 && cd project002 && git init)

To check if the current current path is within a git repository, simply run git status - if it's not a repository, it will report "fatal: Not a git repository"

You could also list the .git directory, and check it contains files/directories similar to the following:

$ ls .git
HEAD         config       hooks/       objects/
branches/    description  info/        refs/

If for whatever reason you wish to "de-git" a repository (you wish to stop using git to track that project). Simply remove the .git directory at the base level of the repository.

cd ~/code/project001/
rm -rf .git/

Caution: This will destroy all revision history, all your tags, everything git has done. It will not touch the "current" files (the files you can currently see), but previous changes, deleted files and so on will be unrecoverable!