It's really not that uncommon for a couple to break up only to discover that they were meant to be together. It's also fairly common for only one partner to actually see the relationship that way. If you're a man and you recently split with a girlfriend, you may just now be realizing that she's the woman you love. If you want to start dating an ex girlfriend again you've got to develop an approach that ensures that she welcomes you back with open arms instead of shutting the door on the possibility of a renewed relationship.
The first crucial step you must take if you want to start dating an ex girlfriend again is to become her friend. Women typically want to remain something connected even after a split. In most cases it's the woman who suggests that you two stay friends. If you're still crazy about her, being just her friend is not going to have that much appeal. It's important to jump on this chance to stay in her life though. Even if she does not see you as a romantic partner right after the break up, if you prove that you can be a trusted friend, she'll be more open to more.
Once you do set up the foundation of a friendship, feel free to ask her out. You need to be careful with this though. If you ever want to start dating an ex girlfriend again you need to begin by asking her out in a non-threatening, purely platonic way. So instead of inviting her for a romantic dinner for two, you should ask her out for a coffee with friends or to a party where they'll be a lot of people she'll know. Make it clear, without being overly obvious, that you're looking forward to seeing her to catch up. You'll be able to sense when she's open for more than just friendship. Until then, respect her as a friend, and she'll start to rediscover all those romantic feelings for you again.