I have an idea for a non-existing web-app I'd like really like to exist and be used by me and others. I could probably start something with my low-level amateur design and programming skills (never learned this systematically), but I believe the project's chances of coming to life are higher as an open-source project that more professional people are leading.
Can this happen? Or, to be more concrete, has this ever happened before with an actual published app or software? Where should I start?
To be clear, I aim at an open, free use application without an intention to sell.