First off , when relationships don't work the first time I rarely ever think about getting back together. Not any time soon ,anyway.
Say after 2-3 years when you both will have dated other people and still believe that you are the best match for each other , miss each other , than yeah , a second shot at it would be good because you both have a different , healthier perspective ,more life experience and a + to the "I know what I have and will appreciate it this time" factor.
What you should do ?
Go NC(No Contact). Now,some people misinterpret this.No contact doesn't mean not initiating conversation with her. It means cutting every form of visual / audio or written reminder of her.
-If you have her SPAM ID , delete that shit.You don't need your eyes glancing at the bottom right of your screen everytime someone comes online , just to see if it's her. At some point you will , she'll be online and you'll start wondering what she's doing / who she's talking to , you'll see her profile picture , you'll secretly hope she'll start a convo with you...all those things are very unhealthy. Delete the contact ID and feel liberated.
-Facebook. Same shit. Unfriend her. Why ? You DO NOT need to see her profile updates , pics she's taking in clubs or whatever with this guy or that guy. You don't wanna see her conversations with other people either. And most importantly , you do not want to see when / if her relationship status updates. Unfriend her and unfriend most of her friends which you don't care about. She might get tagged in their pics. Again , all this only contributes to mindfuck and nothing else.
-Phone number. If you think you can control yourself,no reason to delete it. I didn't delete my ex'es number when we broke up , I never was the 'drunk caller' . When I'm drunk I just don't give a fuck and hit on anything that moves (almost) , I'm a happy drunk as opposed to the sad ones. Anyway,it's your call here.
-Photos / emotional gifts (stuff like stuffed animals , love letters , you get the point). Destroy them or banish them. If you don't wanna destroy them (I didn't destroy mine. It seems stupid to destroy any evidence of 3 years of your life -my case- or 1.5 of yours) put everything in a box and stash it somewhere you won't stumble across them on a daily basis. I stashed it in my garage.
-Clothes. If she got you a cool t-shirt / dress shirt / shoes / stuff like that ,no reason to give it up. Wear that shit if you like it. I have no problem wearing clothes she bought me on different occasions. But again,if you find it difficult , stash those away too.
-Sex tapes / hot / nude pics of her or of you both. That shit has to go. Either you delete them or put them on a flash drive which you bury in cement under the foundation of your house. This is the first and most powerful 'regret' a man will have. My best friend went through a brake-up about 9 months ago (he had 2.5 years with her,something like that). The idiot didn't delete his home made porn with her. Needless to say he was jerking off like a dog and then would fall in a vicious depression. Eventually I convinced him to move everything on a flash drive. He then gave it to me ( he said he wants me to kick him in the balls if he ever asks for it back and I consider he's not over her). To this day I still have it. That girl was insanely hot and for 9 months I'm still not sure weather I should take a look or not. I REALLY wanna see that chick naked but something about seeing my bro's dick is very unsettling. I probably won't do it.

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When you clean these things up , make sure you did it properly. I recently found a love letter from my ex with whom I broke quite recently in one of my books that I did not open in 1.5 years. Needless to say I was pretty fucked up after seeing and reading it. I felt like running back on my knees to her - thank God I didn't. Anyway,make SURE there's no reminders left.
-Music. DO NOT listen any song that makes you think about her. Nothing about heart brake / cheating girls / love. Nothing like that. Spend 10 hours on making a pump-up playlist. Put in there songs that get you fired up. For me rap & hip-hop works the best. Those beats turn me into an animal and I feel invincible. Play me a love song and I'm on the floor rolling in tears. I exaggerate ofcourse , but my point stands. You might think you find closure in love songs , but you're only torturing yourself. Your mind is very flexible. If you surround yourself with positive music , and a positive environment ,you'll find it much easier to get over her.
-Hobbies and Passions. Definitely work on those. Hit the gym like a beast , learn a new dance style if you're into dancing , learn MMA. Pretty much any physical activity will release dopamine and endorphines. You want those , it will keep your mind happy and positive. You will relapse from time to time and find yourself in a dark spot. At which point your pump-up playlist should be used to it's full effect.
-Don't masturbate. Seriously just don't. At all. I mean NO FAPPING. For how long ? For as long as you can. I mean that ! If you can reach 3 months,YES 90 DAYS , you're golden. I realized that after my brake-up , during the orgasm and a few minutes afterwards you're all "Fuck her,I'm so good without her". 5 minutes later your curled up in a ball sad and pathetic. The higher your testosterone levels are , the more emotionally stable you'll be. I haven't wrestled with the snake for almost 30 days now. My sex drive is through the roof and I feel invincible. Also , you feel an unstoppable urge to go out and socialize whenever you see a sexy pic. If you're out and see a sexy girl , you'll be all over her.
The best part ? That emotional stability I was talking about.You won't feel as sad and pathetic any more. Not even close. Add to that the energy boost you'll feel and you're golden.
Don't think it's easy though. Every time I see a hot pic on facebook my hands shake. I wanna devour that shit.The temptation will seem unbearable at the time. Turn it into motivation to do...well,anything , and you'll be very happy.
-Lastly , being single after all that time will enable you to 're-acquaint' with yourself. You'll find it pretty awesome to be single again. You'll think of her less and less and start enjoying your own self more and more.
With NC , if she initiates a convo with you , you can either ignore it or respond. But responding is a thin line to walk. You might relapse pretty nasty. If you do respond , keep it short and casual. Anything beyond that should be shot down immediately.
Again,a failed relationship is failed. Think of it as a car. You buy a car and you don't really like it. It doesn't suit you. Would you buy that same car again ? or would you rather go out and try different brands ?
After you tried several other cars and you're not as pleased with any of them as you were with the original one, you might consider buying it back. But at least now you come from a place of abundance and actually know how good it is,right ?
Besides , there are tons of different brands and models , chances are VERY HIGH you'll find one that suits you great,if not perfectly.