Food
How you eat, and what you eat during a Century will have an important bearing on your results. You must refuel (eat) and rehydrate (drink) sufficiently, in order to sustain enough energy to finish.
A typical cyclist will burn about 500 calories per hour. So if you're in the saddle for 7 hours, than you'll burn about 3,500 calories. That's equivalent to 1lb of body fat or more than a full day's total caloric intake for the typical person - usually 2,000-2,500 calories.
It's important that you replace the calories while you ride, however, you don't want to refuel with the foods that you would eat on a normal day. They contain too much sugar, too much fat, and not enough carbohydrates. Endurance sports such as long-distance cycling require the intake of a greater percentage of carbohydrates than you would normally consume.
I'm sure you've heard of marathon runners that "carb-load" the night before a race. Eating lots of pasta, builds up a store of carbohydrates that their bodies can burn throughout the race.
Cyclists don't necessarily need to carb-load. You just need to make sure that you're consuming enough carbs throughout your ride. Century rides will typically offer carbohydrate-rich foods at rest stops - breads, muffins, bagels, Fig Newtons, etc. These are the types of foods you should be eating during your ride. You'll also see peanut butter and jelly sandwiches, because peanut butter has about 3.5 grams of carbs per tablespoon.
Fruits such as apples (10 grams), oranges (8 grams) and bananas (26 grams) are especially good to eat as well. They provide carbohydrates, nutrition and hydration, all in one. Because of the high carbohydrate content of bananas, they've become the number one fuel of serious cyclists. You'll often see bananas in the back jersey pockets of riders.
Rest stops will offer other foods and snacks such as granola bars, pretzels and peanuts, which are also good for refueling and quenching your hunger. Centuries may also offer sweets such as cookies, candy or pies. Just be sure that you eat these later in your ride, not early. The extra sugar won't do you any good early in the day, however late in the day (your last rest stop) it can serve as a treat or reward for your accomplishment.
Water
Keeping hydrated is especially important. It's often said that "you need to drink before you're thirsty, and eat before you're hungry", when riding a Century. If you don't drink enough fluids, than you run the risk of dehydration. And once you're dehydrated it's too late. You won't be able to "drink more" and rehydrate because the damage is already done. Your body will need hours to catch up on it's fluid requirements, so continuing to ride while dehydrated can become a health concern.
How much you actually need to drink during your Century will depend upon several factors, with temperature being the most important. In hot weather you'll sweat more and need more fluid replenishment. In fact you may need to drink twice as much on a hot day. How many hills you encounter, how much shade you have vs. hot sun, your body weight, etc., all have a bearing on fluid replenishment requirements.
Therefore it's difficult to come up with an exact formula for how much you'll need to drink. Your best way of knowing the answer is to keep track of your fluid intake on long training rides. Weigh yourself before and after each ride, to be sure you've been drinking enough. If you've lost weight, than you're not drinking enough. If you've gained weight, than you've been drinking too much.
Studies have shown that the rate of water loss through sweating is nearly the same as the body's rate of water absorption, about one to three quarts per hour. That's the same as one to two small water bottles of water you're losing.
So how much should you drink during a Century? The best answer isn't how much, but how often. Take a sip of water every 15 minutes whether or not you're thirsty. It's more important to continually replenish your fluid intake, rather than drinking a lot, only occasionally.
Chances are that you'll go through one water bottle every 10-20 miles. Therefore you'll always want to carry two water bottles (or a Camelbak) for your Century.
Gatorade
You also need to replenish electrolytes, sodium and potassium salts, which food and water can't supply fast enough during your ride. That's where Gatorade comes in. It's vital for keeping your body hydrated during strenuous exercise, so you'll find Gatorade at Century rest stops. Since you need to consume Gatorade in addition to water, many riders do this by carrying two water bottles - one for water and one for Gatorade.
Summary
If you've ever heard of the terms "Hitting the Wall" or "Bonking", than you know what happens when you don't fuel properly during an endurance event. Your body simply shuts down and you can't go any further. It's important that you eat enough carbohydrates (30-60 grams per hour), drink enough water (sip every 15 minutes) and rehydrate with Gatorade, so that you finish your Century strong.