I know some people download the apk files because they don't want to pay but there are a few other reasons like downloading an app that is not available in your local store. I had to download Pandora, a free app mind you, from another website to install it because it's not in my Google Play store.
On Topic: To install it just connect your phone to your PC and choose to use it as a hdd from the options. Then copy and paste the file into a folder, preferable your downloads folder. After that use Astro (free file manager from the store) to go to your downloads folder where you can click to install it. Hope this helps.