Before joining a Zoom meeting on a computer or mobile device, you can download the Zoom app from their Download Center. Otherwise, you will be prompted to download and install Zoom when you click the link to join a meeting. Just follow the instructions, and of course say “yes” if it asks you if you want to allow access to things like your audio or microphones.
You can also join a test meeting to familiarize yourself with Zoom.
If you want to know what to expect on joining with your particular device, find it on this page: