You may be tempted to shower her with lavish gifts, such as jewelry and flowers, but for many women these gestures feel shallow, almost like a bribe.
Instead, show her how much she means to you by creating something just for her. Write a list of your favorite memories of her, or the things you love most about her. Make a photo album of your favorite pictures of the two of you, or a mix CD full of romantic songs that make you think of her. Better yet, if you're musically inclined, write a song for her. If you can't carry a tune, try writing her a love poem or a love letter. Write it out by hand, the old fashioned way, instead of through email. Don't be afraid to show your emotions; if you truly want to win her back, you have to be willing to put your heart out on the line.
Maybe there were things you know you could have done better in your relationship.
Perhaps you didn't help out around the house as much as you should have, or maybe you didn't pay enough attention to the things that interested her. If this is the case, then you may need to show her that you've changed in order to win her back. Let her know that you have been taking dancing classes or reading some of her favorite books, or that you stopped smoking, learned to cook, or that you finally cleaned up your garage. Sometimes the practical things you do to show her that you're trying to be a better partner can be the most romantic gestures of all.
You could always opt for a recreation of the infamous Say Anything scene, but you might lose points for unoriginality.
Still, if a grand romantic gesture is what's in order, try hiring a sky writer to write your plea in the clouds, or run an ad in her local newspaper asking for another chance. You could also mail her a letter each day listing one reason why she should give you another shot, or learn to cook her favorite meal and invite her over for a romantic dinner.
Perhaps most important of all, be honest with her and with yourself about why the relationship wasn't working to begin with, and know when it's time to throw in the towel and move on.
Sometimes a woman doesn't want to be won back, and you need to know if that's the case. Don't pester her, or make her feel uncomfortable. If she really wants to leave, then you must let her go.