I downloaded an app, but how do I install it on my device?

Out of the box, Android does not allow installing apps through any means other then the market that comes bundled with it. You first have to allow the system to accept APK files from "unknown sources". To do this, simply open your Settings and check "Unknown sources" under "Security".

Once you have done that, you need to transfer the APK file to your phone. How to do this depends on your particular model. One way is to simply copy the APK to the Downloads folder on your SD card and "run" it from there through a filemanager.