The field of analytic combinatorics in several variables (ACSV) develops techniques for studying multivariate generating functions, which encode combinatorial structures with multiple parameters tracked. In this presentation, we describe a collection of methods for computing asymptotics of multivariate algebraic functions, including techniques for embedding the generating function into a higher-dimensional rational function, explicit contour deformations and implicit integration on algebraic varieties. Examples highlighting these techniques on a variety of applications will be shown, as well as implementations of each method in SageMath. This is joint work with Torin Greenwood, Stephen Melczer and Mark Wilson.