Some familiarity with git tags and branches may be useful. Git Basiscs - Tagging is quite good.
A Microsoft Windows machine for testing and BuildingPythonWindowsExecutables; that subpage also contains help how to install Python, utilities, and a Subversion client under Windows.
Access to update the PyPI transitfeed package. That means, you need an account at that site, and an owner of the package needs to grant write access to you or do the update for you.
Steps
Ensure that all tests pass.
Bump the version number in transitfeed/version.py
Tag the version: git tag -a X.Y.Z -m "Tag for X.Y.Z release."
Publish your tag: git push origin X.Y.Z
Create a new Release in GitHub
Create release notes from the commits and issues that were included in the release.