I found a fledgling, so now what?

So I was in my back yard and under a tree I found a robin. It is obviously not full grown since it can't fly and still has many fuzzy down feathers. I put him in a box, mainly to rescue him from my little neighbors (who would grab him no doubt) and my cat. I called a rehabilitation center, and the woman there said to feed it soft cat food (which, luckily I had) Now I have it the box in my garage, it has water and I fed him, but now what? It's mother perches nearby but won't come near the box where her baby sits. Should I just leave it out on my lawn and let it do whatever God created it to do? If not, how often do I have to feed it? Should I try to find it bugs? How will it learn to migrate and feed itself?