With a lot of Mac apps, they come in a .dmg file, which is basically like a .zip file for Windows. That's not entirely accurate, but it's good enough for our purposes. Anyway, once you open that, then there's a window with the actual program inside it. You just drag that to the Applications folder, and you're done. You go to Applications and run the program. Simple as that.

The App Store for OS X takes care of all that for you, so it's even simpler. Very few apps, generally only really large ones like MS Office or Adobe Creative Suite, will require any kind of Windows style installation.