you cannot make your site as facebook app but you can make your website part of facebook graph network which means your pages will appear in facebook if they have enough person to like them visit this link to understand more developers.facebook.com/docs/reference/api/
You can create an app within FB and place it in your site, if that's what you're asking. Just Google apps on Facebook.com. (sorry I can't place live link yet)
Do you mean you want to create FB app and use it on your site - like a FB comment or something? If so, you can check out it with Facebook developers
You can take help of third party sites like Wildfireapp dot com which help you creating cool stuffs in FB, twitter etc..
By the way, there are a few companies out there that do a revenue split, where they will build your app for you in return for a profit share might be useful if your trying to do things on a tight budget