How do I list the content of a PPA that I have added to ubuntu?

I just added a ppa like so:

sudo add-apt-repository ppa:stebbins/handbrake-releases

Now, how do I get to see which packages this PPA contains?

I'm sure there is many ways to do this - since you have added the PPA, the package details exist in /var/lib/apt/lists

Thus for your example ppa:stebbins/handbrake-releases

substitute / for an _ and remove the prefix ppa: i.e. stebbins_handbrake-releases

Then just use this repositoryname in the following command line entry:

cat /var/lib/apt/lists/ppa.launchpad.net_[repositoryname]_*_Packages | grep "Package:" | sort | uniq

i.e.

cat /var/lib/apt/lists/ppa.launchpad.net_stebbins_handbrake-releases_*_Packages | grep "Package:" | sort | uniq

On newer versions of Debian the Packages file is LZ4 compressed, so you'll need to apt-get install liblz4-tool and then insert an lz4cat step into your pipeline to decompress it:

lz4cat /var/lib/apt/lists/ppa.launchpad.net_stebbins_handbrake-releases_*_Packages | grep "Package:" | sort | uniq

This will list the contents:

Package: handbrake-cli
Package: handbrake-gtk

To see the content of a ppa you can use Y PPA Manager. Install it by running the following in a terminal:

sudo add-apt-repository ppa:webupd8team/y-ppa-manager
sudo apt-get update
sudo apt-get install y-ppa-manager

When the application is started, click on Manage PPA's:

Select the PPA you want to see the content of:

And finally click on "list packages" to see all packages provided by the given PPA.

Hopefully this will help.