A small bowl (coffee cup size) of water will suffice. 

1.  The Pigeon will eat any type of bird seed or corn. 

2.  A (temporary) 2 foot sqaure wire cage will work fine. 

3.  Don't be afraid to handle the found pigeon. 

4.  The worst you can do is ruffle feathers. 

5.  By the way, Pigeons don't bite. 

Care of Found Pigeons: 

Most lost birds are hungry and thirsty. Water is necessary before all else. Since pigeons drink by suction, any water container should be at least 1 in. (2.5 cm) deep. An open container, i.e., a dish, an old margarine container tub, etc., is best. While a thirsty bird may drink immediately, it also may not. A bird, which has gone without water for a while, is sometimes a bit less than itself. It may be so exhausted; it doesn't even realize that water is in front of it, especially if the water container you use is different from what it is familiar with. A trick I've often used is to trickle a few drops of water from on high into the container to make a splashing sound. When they hear that, most birds will invariably head to drink. If a bird looks really exhausted, Gatorade or other proprietary sports drink may be added to the water. A teaspoon or two per cup (250 ml) of water will help replenish electrolytes. 

Pigeons are grain eaters. While park pigeons will eat bread, most domestic birds have been raised on a multi-grain mixture and have never seen a slice of it. In fact, they would likely ignore it as possible food. Instead of bread, you might try feeding them something else from around the house. Popcorn (maize), rice, split peas, barley, buckwheat (kasha), canary seed, etc., are all good first options to feed a lost bird with. THESE GRAINS SHOULD NOT BE COOKED OR POPPED BUT FED RAW. Water should also be provided since pigeons normally drink immediately after eating. 

Any container that a dog or cat can't get into will be fine. An old bird cage will hold the pigeon for a day or so with no problem, as will a cardboard box - a screen on top of such a box is better than simply closing the flaps since there will then be enough light for the bird to see to eat and drink.