How can I take care of my liver now as it was a reason if too early birth of my child?

Exercise . Avoiding anything in excess that is known to be toxic to the liver is obvious (tylenol, alcohol, etc...). However, it's equally important to maintain a healthy diet and exercise 5 days a week. Be sure to have a good history and physical exam done by your physician as well as labs to look at liver function tests and cholesterol.
Liver. I think eating healthy and including more organic foods in your diet will help. Exercise is just good for our bodies. And of course, try not to use and medications that can harm your liver. Know that some of the liver problems are specific to pregnancy, so you may need to ask you OB about problems in future pregnancies.