Try this reference https://arxiv.org/abs/1105.5759 (Notes on "Quadratic Forms and Automorphic Forms" from the 2009 Arizona Winter School, by J. Hanke).
P.S. See also http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.543.8732 (A proof of Siegel’s weight formula, by A. Eskin , Z. Rudnick and P. Sarnak) and https://www.youtube.com/watch?v=b3qDTu0C7dM (a video of Jacob Lurie's lecture "The Siegel Mass Formula, Tamagawa Numbers, and Nonabelian Poincaré Duality").
One more interesting paper is https://www.researchgate.net/publication/2404971_Low-Dimensional_Lattices_IV_The_Mass_Formula (Low-Dimensional Lattices IV: The Mass Formula, by J.H. Conway and N.J.A. Sloane).