How do I get my ex girlfriend back?

Is it worth being sad over someone who doesn't want you? She wants to be single now, so you should accept that and move on with your life.
Don't waste your sadness and beg for her to come back. If she wants to come back to you, she would let you know. But the main part of moving on is to have a different mindset. The mindset where you think she will NOT come back. I think you should move on.

First you must take the lead, and be the mature adult when arguments start. Go to great lengths to avoid confrontation, but if it comes then maturely deal with it.
Surprise her with your change of personality.
Now for the break up.
Patricia's right, romance her indeed.
A fancy date, nice meal, a red rose, perfume, and a special card to say how sorry you are. Take 100% blame even if it wasn't totally your fault.
But as I said, in a turbulent relationship, one partner has to be the more mature one, so show her your best Prince Charming routine, but most importantly, treat her as your own princess.

Ask her out on a proper date somewhere nice and make the date all about her.

Romance her!