More importantly - I just stopped doing those kinds of projects altogether. Why? Because you should do what you enjoy. Regardless of how much money you think it can make. Wasn't that the whole point of working for yourself in the first place?
If nothing comes of it, that's okay. At least you enjoyed yourself. The worst possible scenario is that you do something you're not enjoying and also don't make money - you have total control over one of those variables, as your own boss.
How do you find customers? (I.e. people with buying power, and clearly defined unsolved problems.) Being able to do so is a pretty valuable skill!
As for finding people to share your product with, it's very easy. If you had any hypothesis behind your solution, you can guess where your customers might be - and if you just approach these people (whether online or in person, such as what the Pinterest founder did), very few will refuse to give your product a try if you offer it gratis. Getting people to pay comes after getting people to love your product, and the latter is difficult enough that if you really did it you won't have to worry about the money.