Wait until you are stronger emotionally.
It is important after the breakup to have some time to think.
You need time to get your head leveled out, and let things cool down emotionally.
One of the most important things to do is accept the breakup.
Stop trying to pretend that it didn't happen or that it's not real.
Accept and even agree with it, whatever the reasons.
It may be that you can get back together with your ex soon enough.
It'll be time soon enough for you to try to contact your ex again.
You may need 2 weeks, or you may need a month or even two months.
Do your best to determine if you are emotionally ready to talk to your ex without getting emotional or trying to argue about the breakup.
Ask her to have lunch with you.
When you're ready, call your ex and ask her to have lunch with you.
Make it a fun time where you talk about the positive things of life.
Don't rehash old arguments.
This is not a time to have "the talk," or try to address blame for why the relationship didn't work.
Again, focus on having a good time, and try your best to have a patient and humble attitude about reconciling with your ex.
Avoiding the appearance of desperation.
You don't want to appear numb, like you think you don't need her, or that you think you're better.
In my opinion, that type of attitude doesn't work, and is not best for the health of the relationship.
However, there's the extreme on the other side too.
You don't want to seem desperate, and you don't want to try to beg to get things back together.
You don't want to rush things.
Try to have a couple coffee or lunch "dates" before you try to get into serious talks about bringing the relationship back together.
Be patient and keep looking for signs that there is even the possibility of a reconciliation.