Deploying an open-source package to PyPI involves several important steps that enhance both functionality and usability. The process begins with creating a Python package, such as the PyBitesTips class, which utilizes methods like `__call__` for callable classes and `namedtuple` for data handling. Testing is streamlined by separating tests into a dedicated subdirectory and using mock data to simulate user interactions. The `setup.py` file plays a crucial role in making the project pip-installable by specifying dependencies and supported Python versions, and the `entry_points` feature enables the package to function as a command-line interface application. Uploading the package to PyPI involves creating distribution files, first testing on Test PyPI, and then publishing to the main PyPI server, with the use of tools like `setuptools`, `wheel`, and `twine` facilitating this process. The guide suggests maintaining a `.pypirc` file for easier authentication and highlights the evolving landscape of Python packaging, where alternatives like Poetry and `pyproject.toml` are gaining traction.