The Fermi mission provides a suite of tools called the Fermitools for the analysis of both LAT and GBM data. This suite was developed by the FSSC and the instrument teams. Originally called the ScienceTools, the suite was renamed when the software hosting and distribution were changed to use Github and Conda. In addition, the GBM team has developed specialized tools for analyzing GBM data, and the FSSC maintains a library of contributed software developed by the Fermi user community, such as Fermipy, that may be useful to your analysis.
You may want to look at this overview of how the Fermitools work and what they do. Then, you can:
You may also want to subscribe to the fermi-soft mailing list to keep up with new software releases and related notices.