That's a tough one, and while it is not an area of professional expertise, I've been there personally. Here's 10 things I learned:
1) If possible make sure kids have equal time with each parent and don't let them wiggle out of time with either. When I divorced and entered a new relationship way too soon, I gave my 12-year-old the option of staying where she felt most comfortable given her closeness to friends (I moved 8 miles away). Big mistake. She took me up on it and three years later she now tells me that she felt abandoned by me. We talk easily about it now and she is with me now as well, but it was a painful time. I thought that was what she wanted, but what she really wanted was for me to push back and tell her "I love you too much not to fight to have you equal time".
2) Kids will "favor" one parent or the other depending on how they are feeling in a day or what they want and will start to pit parents against each other. I think this is human nature, because it has happened to everyone I know who has gone through it. The parent perceived as "the one who left" or "the one who caused the divorce" may get a lot of angst tossed at them. Tell them you understand they are upset and that you are always happy to sit down and talk about why the divorce is necessary. Best if you can do it with the other parent present. Always put up a united front: "We decided....this is the best choice for both of us and we think for you so that we all have the chance to reach our full potential."
3) Set the same rules -- curfew, attitude-checks, consequences, TV time, etc--at both homes. Keep open lines with your ex about how they are being enforced and STICK to them! We have different rules for a while and it was chaos. Kids, even teens, need structure, especially if they are shuttling back and forth. And by the way, make things EASY in that shuffle by investing in close and toiletries at both houses so they do not feel like vagabonds.
4) Give your kids a metro pass and let them show you they are independent by learning the bus system. This helped my daughter to see our divorce as a form of new independence for her. She travels back and forth between us now easily and loves the freedom. She must call or text us whenever she is on a bus and must check in with one of us every couple of hours.
5) Consider monthly family meetings to check in and see how rules, feelings etc are going. Don't let your teens bag out and set the expectation that they must bring three pros and cons of their experience to each meeting. Give them power in these meetings to run the meeting or set some ground rules of their own. A friend of mine also has Family Dinner once a week with her ex, his companion, her companion and the kids. All must be there. It has done wonders for relationships.
6) Do NOT talk ill of your ex and do not let the kids do it. Even if he or see is a piece of work, they are your kids' parent. Be respectful at all times as a model to your teens.
7) Set specific homework time, curfew, attendance at meals rules and stick to them. Otherwise, let them spend ample time with friends and in activities. I made the mistake of not demanding my teens sit down to dinner and their dad did -- and let me tell you he got the better of the deal.
8) If you start to see rebellious or disrespectful behavior, sliding grades, self-abuse, insist on counseling, EARLY. Divorce is a grief process any way you cut it. Give them a place away from you to grouse and rage -- and learn coping skills.
9) BEFRIEND YOUR EX. Even if you can't stand him or her. You don't have to live with him or her any more so what's the point in fighting? Your solidarity, especially around the kids will go MILES in helping them adjust.
10) Talk to them. A lot. And listen more than you talk. REALLY, listen MORE. Validate your teens experience and perspective and show them you learn from them as they learn from you. Neither of you is the expert in divorce.