Whether you broke up a month before or a year ago, there's always a way to get back the woman you had loved.
Since the breakup has happened, there were definitely some misunderstandings and mistakes that took place. The word you're looking for here's retrospection. Before going any further, be as objective as you can, and figure out what went wrong. Be sure to remember the old adage of 'when you point the finger at someone, you have three pointing right back at you.' No girl is going to take you back if you've no clue why you guys broke up.
After having that discussion with yourself, if you still want her, then it's time to reach out and contact her. Call and ask her if she'd like to do something non-committal, like having a drink with you or go out with you for a cup of coffee. You can choose to email her, but make sure the message is light and playful. Saying things like 'I can't live without you' or 'I want to get you back' can be too overwhelming and she might not meet up. If she rejects your advances at first, don't be too desperate and respect her decision. Given space, chances are, curiosity will get the better of her and she might end up saying yes to you.
Despite who actually initiated the breakup, the fact is, there are reasons behind the breakup. Make sure you improve on the things that she complained about before meeting her. Why? Because when you meet her, you want her to regret her decision. Show her that, you're a changed man. You want to show her the guy she fell in love with, not the guy she broke up with.