While there is no way to ensure that you will always get along with your ex, it is really the best thing you can try to do for your children. There are several ways that you can make this possible, regardless of your differences. By keeping communication open, not arguing in front of your children, and trying to see things from their perspective you can really cut down the arguments!
So, how do you get along with your ex? It is as important now to communicate effectively with your ex as it was when you were with them! You have to know what is going on in your childrens' lives while they are with the other parent, and often misunderstandings and problems arise simply because there is not proper communication. When you pick up or drop off your child, take five or ten minutes to discuss what will be happening or what has happened. When something happens, inform the other person right away. Even this small bit of communication can save hassle and frustration for everyone involved, especially your kids!
It seems like it would be common sense not to argue in front of your children, but just about every single parent has had it happen before. It is important, though, that you provide a united front to your children. Not only will they know that everyone is acting in their best interests, they will also know that you are making an effort to get along for their sake. They will know that they cannot play one parent against the other. They will understand that, while you are not a traditional family living under one roof, you are still functioning as a family in terms of making decisions and sticking to them. If you must hash it out, don't do it where your kids can hear you. Hearing parents argue is harder on children than they let on.
If you have ever thought to yourself that your ex does not understand your position or your circumstances, look at that the opposite way. Do you understand where they are coming from? Do you understand why they are being argumentative? It is hard to expect someone to see your side of things when you are not seeing theirs. If you step back for a moment you can often think of things from the other person's side. Are they asking to drop your child off later than the original plan because they want to inconvenience you and throw off your schedule, or do they want to because they want more time with their child? Would you want more time with your child in their situation? Now you see things from their perspective, and it's hard to be mad at someone for wanting to see more of their child! This is only one example, and this technique can be used in almost any situation that arises.
The truth is, nobody gets along all the time, but with these simple steps it is easier to get along for your own sanity, and for the sake of your kids.