There are a lot of mysteries on this earth that defy explanation. One of them is - how on earth is it that two people meet, become friends, fall in love and think the world of each other, share their most intimate secrets, make love, take the big leap and get married, settle down, have children, buy a car, get a mortgage, have disputes, get on each others nerves, erupt into arguments, contemplate divorce, get a divorce and are now sworn enemies for life?
Given a choice, most 'former' lovebirds would choose to live as far away from each other as possible - like at separate ends of the equator. But the divorce settlement usually comes with shared responsibilities such as alimony, joint child custody, etc. As such, there never really is complete separation, and it would be best for both parties to make the effort to make the best out of their new relationship.
The first thing you have to realize is that COMMUNICATION is key. I know. the lack of communication may very well be one of the reasons why you got separated in the first place but surely now you realize that it IS a factor that any good relationship cannot live without. A cardinal rule in keeping the communication lines open though is this - never, ever bring up the past. That's where all the problems came from, so keep everything in the here and now.
Next would be ACCEPTANCE of the situation. Acceptance is the red carpet to establishing even at least a semblance of a cordial arrangement. Accept the fact that the relationship went wrong and that both of you are to blame. In short, hold yourself accountable too for the dissolution of your marriage and do your part in this reconnecting stage in your lives.
FORGIVENESS is as important, if not more important, than the first two. Communication and acceptance won't work if any or both parties still harbor a grudge against each other because the negative emotions will only make the atmosphere harsh and confrontational. Never mind forgive and forget; nobody really can forget something that happened unless one has amnesia. But to start forgiving each other (and even yourself?) is a good start.
Remember that your idea of reconnecting with your former partner may or may not be what he or she has in mind. at least, not now. If such is the case, do not push it. You may end up doing more harm to your newfound relationship than good. Instead, give each other space.
Believe it or not, the cliché IS true. time does heal all wounds. No matter how disconnected you are with your former spouse (or vice versa), take heart in the fact that more often than not, nature will step in and take all the negative emotions away. all in due time.