Try it out
You can try out Macaulay2 in a web browser at web.macaulay2.com. The web application running there was written by Franziska Hinkelmann, Lars Kastner, and Mike Stillman. Read the "Welcome Tutorial" there to find out how to interact with Macaulay2.
You can also try out Macaulay2 in a web browser on the Sagemath cloud, thanks to William Stein. Create an account, log in, create a new project, create a new terminal, and then run "M2". Refer to Getting Started for ideas about what commands to try out.