Welcome to the forum, Julie! My first recommendation is to go to
www.finchinfo.com, where you will find many articles on housing, diet, breeding, and species. If you put your general location in your profile, it helps when answering locale-specific questions later on.
What species finch do you have? Photos will help members identify them for you if you don't know. I will assume they are either Zebra finches or Societies, since those are the most common. Both species also will breed like rabbits, so unless you want to be overrun with babies, it is better to remove the nest.
It sounds like the baby fledged, which is what happens when it is old enough and strong enough to leave the nest, but it still can't feed itself. The parents will feed it for another couple of weeks until it is weaned, which means it can eat and drink on its own.