nothing in this world is for free man, you gotta whip out some money to get anything worth while.. There are some free services out there that will let you create apps for free on their servers but they put their banners on there and you get paid sqat (pretty much you do the work to make them money) Best advice, save up, try and learn to code php, mysql, ajax and keep read alot on the facebook dev forums and maybe try and learn how to create your app from that..
agree! also consider shelling out some cash for a script like phpfox (my preference) or social engine (which i've never tired)...and use your ajax/php skills to customize it.
What sort of App are you looking for for free? I can provide a free app if you pay for the hosting with us which is $10 per month for a quiz app, $20 per month for Riddles app, $50 per month for an RPG. Samples of the above are as follows: http://apps.facebook.com/britishpubquiz/ Not launched yet. http://apps.facebook.com/riddlesforme/ Making around $20 per week http://apps.facebook.com/stargateextreme/ Making around $40 per week http://apps.facebook.com/merlinsadventure/ Nothing yet as not launched Whilst the figures quoted above are for my apps your apps may vary depending on how much time and effort you put in. Some other apps are quoting massive income and they could be telling you the truth and I presume they have many thousands of app users. The apps i have currently have between 500 and 3000 users so they are pretty small scale. We are more interested in making them than promoting them. Drop me a pm if you are interested.