The best thing to do is leave it alone! The parents will find it and continue to take care of it wherever it is. Baby birds do not leave the nest knowing how to fly. They initially fall out of the nest, and start clinging to branches or brush. The stay close to the ground for about 1-2 weeks, and start flying with short hops from branch to branch. The hops gradually get longer, until the bird eventually flies.
When possible, remove the cat or dog from the area until the bird is able to fly (1-2 weeks). Put the bird in a nearby bush, shrub or tree limb, out of harm's way. Most birds have a poor sense of smell, and the parents will not abandon a baby bird touched by humans. Don't stay in the immediate vicinity of the bird – the parents are probably watching and will not approach if you stay around.
Return the bird to its nest.
You can make one using a small basket or margarine container. Punch holes in the bottom and line the container with paper towel (not with grass, as moisture in the grass can cause birds to become too cold). Secure the 'nest' with duct tape in a branch fork near the old nest. The parents will find it.
When you are certain the parents have been killed, prepare to transport the bird to a rehabilitation facility. Carefully place the baby bird in a small open container linked with paper towel, and place both in a cardboard box. Do not attempt to feed or water an orphaned bird. A bird's diet is very particular and they have a feeding schedule that must be followed.
Do not. Migratory birds, including songbirds, are protected under federal law. Possession of a bird, its nest or eggs, without a permit is illegal.
Here is a useful chart: