What should I do to get my ex-girlfriend back?

You should tell her how you feel because it's important that she knows. But I don't know if having a long distance relationship is a great idea; but then again. How is your connection with her? Do you feel like you guys are really really awesome together, you're madly in love with her and you're best friends that understand one another really well? In that case, don't give up on love just because of the distance.

Remember, there are some people that you can sit next to and feel millions of miles apart from and there are others that you can be a million miles apart from but feel like you're next to one another. If she's the second one, then go for it!

The deal in break-off is that there was something that didn't quite add up to your syncing together. Since its already been 3 months, good enough time for you to get over her; whoever is maturer of the two in this relationship would have.

If you still wanna hang the noose round, you could try finding out the reason the break-up happened; and probably work on a part on telling her why it took you 3 months to attempt a patch up and surely add a pinch of sincerity in the entire op. If you really don wanna look like a dork if the entire deal crashes down.

Let it go. She'll find somebody else, plus, at your age, long distance is hard.