Below are various data analysis tutorial videos generated by the Fermi team to demonstrate standard analysis techniques and basic analysis software usage.
You can watch the videos inline or download them (how to do that depends on your browser, e.g., look at the context menu brought up with a right click).
Joe Eggen covers how to download Fermi data, find documentation, and get started on analysis. You may want to download the Jupyter notebook used in this tutorial.
Joe Eggen goes through a binned likelihood analysis of an AGN. You can also download the Jupyter notebook used in the video.
This video shows you how to analyze a Gamma-ray Burst (GRB) with the gtburst tool. You may also want to read this tutorial for gtburst.
Matthew Kerr demonstrates how to analyze pulse signals in Fermi LAT data.
These videos cover the basic functionality and use of the GBM Data Tools for analyzing GBM data.