If you mean a site apart from the Play store, you will need to set "Unknown Sources". In Gingerbread, this is usually under
Settings>Applications>Unknown sources and check the box. This allows apps to be installed from sources other than the Play store.
Then, you can use the browser on your device to go to the web site, download the app and then install it. You can also use a browser on your computer if you have a way to transfer files to the phone (SD card or USB for example).
BUT....., make sure you that you really trust the web site! Turning Unknown Sources on is considered dangerous as you can easily install malware, it is safer to only download apps from the Play store. Once you have downloaded the app you need, turn Unknown Sources off again.
That said, there are times it makes sense for certain versions of apps that aren't in the Play store, but again, make sure that you understand the risks.