After installing Moom, it should have walked you through the process of granting it access via Apple's Accessibility permissions system. But if that didn't happen for some reason, here's how to give Moom the permissions it needs to work.
macOS 11 and Newer
With Moom installed, open System Settings, then select Privacy & Security. In the long list of topics in the right-side window, find and click on Accessibility:
Within the Accessibility panel, scroll down until you find Moom; once you see it, make sure the slider is enabled:
If you don't see Moom in the list at all, click the "+" sign at the bottom of the list, enter your password when prompted, and then navigate to the Applications folder in the window that appears. Find Moom and double-click it to add it to the list (and grant it approval).
Older macOS Versions
In versions of macOS prior to macOS 11 Big Sur—specifically, macOS 10.13 (High Sierra), macOS 10.14 (Mojave), and macOS 10.15 (Catalina)—enabling Moom is slightly different. When launched, you'll see this dialog:
Click Open System Preferences, and you should see Moom listed; check the box next to its icon to grant it permission to run.
To manually add Moom to the list, open System Preferences, then open Security & Privacy, and then Accessibility. From there, the steps are the same as detailed above: Click the "+" sign, find Moom in your Applications folder in the dialog that appears, and click Open.
Once you see the Moom icon with the box next to it checked, Moom is ready to use.
Troubleshooting
If Moom's pop-up palette doesn't appear when you hover over a window's green (or yellow or red, depending on your Moom settings) window widget, this is usually a sign that the macOS Accessibility system has lost track of Moom's permissions.
There are a number of things you can do to try to kick start the OS, and they're all covered here:
How can I get Moom's pop-up palette to appear?
If none of those solutions solve the problem, please use one of the contact methods at the bottom of the Overview of Moom chapter to get further assistance.