Dating after a divorce doesn't have to be disastrous experience here are some basic tips.
What to do
Talk to the new female/male in your life if you've found someone. Explain to them how you feel about dating now that you are a divorcee. Let them know if you are afraid to fall in love, or not ready for serious intimacy. If you have children, let them know this up front. It's best to be a as honest about your situation as possible. You want to avoid as many misunderstandings for yourself and your potential mate.
If you haven't met anyone, go slow. Some people join dating services, or online chat rooms when looking for love. This is ok, but play it safe. Make sure you make decisions because you are ready and not so much because you are lonely. Picking up people at bars for example could potentially be dangerous. If you have agreed to meet someone that you've met from online dating, bring a buddy along the first few times, and go to a public place.
Make sure you feel like a "whole person" before you begin to date again. You want to have something to offer the other person in the dating experience. If you are still broken, or down because of the divorce you may confuse the other person and be a turn off. Giving yourself enough time to grieve and get to know "you" all over again can help considerably. You will feel more confident about meeting someone, and you won't have leftover feelings for your ex.
If you've come to the point where you want to introduce someone to your children, talk to them first. Your child(ren) may still be grieving over the divorce and may be far from ready to meet someone. Make sure they understand that you aren't replacing your ex. Explain to them your feelings for the new person, and maybe let them in on some positive traits about the other person. Don't force meeting a new love on your children. When they are ready, plan something to do in the kids' favor away from the home. This way they won't get the vibe of "replacement" of the parent who is no longer there. A new man sitting at the table where their father used to sit, or another woman cooking in the kitchen may be hard to swallow for some children. Be thoughtful and put yourself in their shoes.
If dating seems to be going all right and there are kids involved, you may want to let your ex know about the other person. It is important for some parents to know who is around their children. Be careful of this if your ex-spouse is showing signs of extreme jealousy, or resentment. Counseling may be needed if the other person can't "move on." Never date for revenge on your ex.
Join a group for women/men who are dating after divorce. They more than likely will have great tips and advice; and you will have a wonderful support system!