Up until now, on the Mac, you couldn't right-click without using the mouse. That's all changed with macOS Sequoia, which has added a new keyboard shortcut that opens up context menus (those are the menus that pop up when you right-click anywhere).
The keyboard shortcut to right-click on your Mac
In macOS Sequoia, you can press Control-Return on your Mac to open context menus. This shortcut, which was discovered by Mastodon user Nathan Manceaux-Panot, should work anywhere on your Mac. At the time of writing, Sequoia is in beta, which means that you should avoid installing it on your primary Mac, no matter how tempting it is to try new features.
Still, to try this yourself, open System Settings, then navigate to General > Software Update. Finally, click Beta Updates and select the macOS Sequoia developer beta.
Other ways to right-click on a Mac
I've also written about other ways to right-click on your Mac and I'll list them out here for your convenience.
Click the trackpad with two-fingers.
Hold Control and click the trackpad.
Click the right-hand side of the Magic Mouse.
Use the right-click button on your mouse
Click the bottom-right corner of your trackpad (needs to be enabled in your Mac's trackpad settings).
When scrolling with two fingers, press the trackpad with a third finger.
In case you're fully sold on the mouse-free life, check out this Mac app that lets you use the keyboard for every task.