A good starting point is to try out the commands at https://faculty.math.illinois.edu/Macaulay2/GettingStarted/ .
The file UsefulCommands.txt summarizes some useful commands to know in Macaulay2. Below are some additional files which explore concepts from the course.

• Get factorization statistics for using Chebotarev's Density theorem
• Exploring the twisted cubic
• Two ways to implement row reduced echelon form
• Implementing polynomial division

The file PerugiaFunctions.txt collects a number of the functions from above (and some additional functions) in one location. Here is how to load and use this file .