Once you click the invitation link you will be prompted to install Zoom, just follow the on-screen instructions. Alternatively you can download zoom in advance of the event here: https://zoom.us/
No. When you click on the event invitation link the Zoom browser window asks if you want to download it. Ignore that suggestion and skip down to the fine print underneath and click: "If you cannot download or run the application, join from your browser."
https://support.zoom.us/hc/en-us/articles/201362193
https://support.zoom.us/hc/en-us/articles/201362663-Joining-a-meeting-by-phone