Apple has multiple ways of making cash, which one are you referring to specifically? They make cash on hardware, services (warranties), and distribution of media and apps.
It seems to me you are asking, how do I make money from end-users without charging them for my product and not selling advertising.
I know nothing about your business, so it is difficult to say what the possible business models are. You're clearly going to have to think outside the box. Take a look at what secondary information you get from the usage of your service.
For a business I am currently looking at, the actions of the user result in a small yet valuable piece of data for other businesses. The data is not in any way 'user specific', and would actually be less valuable if it were tied to a single user, but I'm considering analyzing the data I get and then selling that analysis to other businesses. Of course you have to be VERY careful with this sort of business model, as you don't want to offend your customers buy sharing any info that they may not want shared. For my industry, it isn't a concern.
However, I would take a good look at what you are offering, who else is in the space, how they make money, and question why you don't want to charge.
A big initial fear I am still learning to get over is the fear that people won't pay, and that means the business is not successful. If app stores, netflix, e-books, etc.etc. have taught us anything, it's that people will pay for what they are able to get for free. People pay for apps, even though the app provides the same info as can be seen on the companies webpage.
My recommendation (and the reason I say this is because I have in the past struggled with the same challenge of wanting products to be free) is to spend time looking at what people do pay for. Talk to other businesses about how customers react to their pricing and business model.
We've were introduced to a 'free-web' where we thought everything to consumers could be free, but it turns out that may have been a bit of a utopian dream, and people really don't mind paying for things.