Three kinds of download:
- .dmg, a disk image. Open it and a window appears with the app icon and, usually, an Applications folder shortcut. Drag the icon onto the folder; that is the whole installation. Then eject the disk image (the ⏏ next to it in the Finder sidebar) and delete the .dmg.
- .pkg, an installer wizard like a Windows setup.exe. Next, next, password, done.
- .app, the program itself, sometimes inside a .zip. Move it to Applications.
The first time you open an app from outside the App Store, macOS checks Apple's notarization stamp and asks once whether you are sure. Apps without a stamp need one extra step; see "Apple could not verify this app".
Uninstalling is dragging the app from Applications to the Trash. There is no Programs & Features. Settings and caches stay behind in ~/Library, small and harmless, and a few apps ship their own uninstaller for background pieces. The App Store's apps uninstall the same way.