I found a baby robin, what do I do?

Yesterday, my dad found a baby robin on the floor under its nest (the nest is about 20 feet above the ground). He grabbed a ladder and put it back in its nest. Then, earlier today, he found it again, lying on the same spot. He had some bird poop under him. He put it in a little basket and had a bunch of Kleenex in it so it would be warm and comfortable. We have been feeding it worms and we have a eye dropper thing for water. Will it survive? It's nest is in our back yard. It has some feathers but still bald spots. We found one of its siblings on the floor, dead, and we didn't want this one to die. The mother kept kicking out this baby robin so we decided to keep it. Will it just take off when its ready to fly? I would hate to see it take off just like that. Or will it just fly around, look for food and come back? You tell me. Is what were doing good enough? Could it survive? We found the dead sibling 5 days ago and it was just newborn. So this one we just found a week old or something? When will it learn to fly? When will it be fledged? Sorry I wrote so much I just really need to know and things haven't shown up quite correct when I asked what I should do.