Getting started with AWS Greengrass is easy. The Greengrass free tier includes 3 free Greengrass Cores for one year.
In order to get started with Greengrass, you will need a device capable of running the Greengrass Core. You can click here to purchase a Raspberry Pi and here follow the easy tutorial in the user guide. There is also a full list of qualified devices here and a detailed set of technical dependencies for using another device here.