Recovering after marathon is as important as tapering and training for the marathon. Without proper recover you increase the risk of injury or overtraining symptoms.
During the marathon, body is pushed to its limit, muscles, tendons, ligament, cell, etc. are pushed to the maximum. Each step your lower body joints, muscles, ligaments and tendons receive your body weight three times bigger. So repeating that force over 42 kilometres distance you can imaging how much destroy it can cause. Also you have higher risk to get flu as your immune system is weaker.

What to do after marathon?
Immediately after the finish line rehydrate, try to get your body back to the normal hydration level, but avoid overhydration. Don’t stop moving, as amazing it would be just to go lay in the ground, move forward, walk! So your heart rate can come down evenly. During the first hour after the finish line, eat something light, bananas, fruits, etc. Eat something that is easy to digest. Eat bigger meal couple hours later.
Go to shower as soon as possible, not only because you probably smell quit bad but taking cold shower or cold/hot shower, changing the temperature hot to cold and back over one minute. This will increase the oxidized blood flow.Rest if the day, just put your feet up and relax. You can go for the easy walk to loose your leg muscles.

First couple days after the marathon, go for the walk or the easy run. It can be only 15-30 minutes. Depending your fitness level, it might feel hard, but light exercise will increase blood circulation and move of metabolic waste. Don’t stretch cold muscles, warm up your muscles first and do only the light stretching. Light massage can be also help to loose tight muscles.

After a week from marathon, increase your training amount carefully, add cross training. After two weeks from the marathon you should be back to normal training.

Main points are the listen to your body, increase your training little by little. Give your body to time recover fully. It’s all depends your fitness level and how much is your weekly amount of running normally.
Don’t stop! It’s okay to enjoy after the marathon, but don’t stop moving. By doing the light exercise will help your recovery process.