To install your package with pip:
$ pip install -i http://my.pypiserver.com/simple/ <PACKAGE>
If you want to fall back to PyPi or another repository in the event the package is not on your new server, or in particular if you are installing a number of packages, some on your private server and some on another, you can use pip in the following manner:
$ pip install -i http://pyppiserver/simple/ \
--extra-index-url=http://pypi.python.org/simple/ \
-r requirements.txt
The downside is that each install of a package hosted on the repository in --extra-index-url will start with a call to the first repository which will fail before pip falls back to the alternative.