After trying to get Google App Engine working locally, I think it's best to ask this question here, and answer it myself. I'm sure some of you might be having this problem.
After installing the GAE SDK for Python, I tried running the tutorial. I cloned their 'Hello World' app from GitHub, and tried to run it locally using dev_appserver.py. I kept getting an error message saying "No module named appengine.api"
I use TensorFlow, and a few packages developed by Google, and found a way to get around this. I will answer below.