I *think* this is how places like techstars work. I had a friend get his business picked up by them and it seems to be working out well for him. From what he told me it sounded very similar. After getting through the screening process, he had some help from them to refine his product and then got a chance to present in front of a bunch of potential investors. From there, he met some people who were able to help him further and is now rolling out his product to clients.
I know how the investors make money and I know how he makes money, but I'm still not sure how the networks make money (in this case techstars). I'm guessing they must get a cut of profits from successful businesses, but I have no idea what that contract would look like. So, you could be looking at a substantial portion of your profits being taken (investors and network). But if you have a good idea and need the startup money, that is one way to get it.
Angel investors invest their own money. Of course they want a return, a big one, since its very high risk. Typically they will demand something like 50% of the company shares, although it depends of course entirely on the type of project. the investor and of course how much you can finance yourself.
As for the network, they dont have that many costs. They just rent some locations for the events, do the prescreening and marketing and give you some assistance. They get their money from the business angels who pay a yearly fee to be a member. As a candidate entrepreneur you also pay a fee, though when I did it, it was only like 50 euro or something, mostly symbolic, and not dependent on whether or not you got financing. IIRC the prescreening was even free.
Then again, different networks will use different rules Im sure.