The best revenge really is going forward with your life and taking the best out of it. What about if the break up was horrible and broke you to pieces? In this case you will have to carry a huge burden with you and you will want to see your ex miserable also. You will hold this grudge inside you...
Live your best life!
But if you want to play it rough there is one perfect way that I'll share with you. But remember that maybe it is not worth it.
If your ex is a female and she left you for someone else in a brutal way maybe she deserves it.
Do you know what a "honey trap" is? When a spouse hires nice woman or man to test the loyalty of the signifficant other? You can do something like that.
Wait in total silence for the honeymoon to pass away, 3-4 monts, a year, you judge it.
Then, hire an attractive woman who will be ready to lay with this guy you were left for. SHe must be cute and able to seduce him, there are this type of girls, believe me... She will know how to get him in bed- in a club, through facebook chat, everything will seem natural and random. The chance the fool will bite are almost 100%, believe me.
Hire a housing where she would invite him, put hidden cameras in advance. There is chance they might not go in the house, so she should also have a camera on her. For example there are cameras in the shape of a cloth button, a medallion, whatever... She will have to mind filming the act, if it goes there. You follow my line, I know.
After that get the recording and make a fake facebook account- send the file to her and everyone connected with her- parents, sisters, cousins, friends, whomever you wish. You must send it to your real facebook profile also. Remember- you must be anonymous and act as if you have nothing to do with that.
Do you imagine your ex's face? You will triumph after that. Well, if all goes as planned your ex or her friends might contact you. Then you say that "what goes around comes around" and you were left for this one... SHe will suffer and wish she never left someone like you who wouldn't do such thing to her.
THIS IS NOT A WAY TO GET HER BACK! THIS IS A WAY TO TAKE REVENGE!
I DO NOT KNOW THE LAWS OF YOUR COUNTRY AND IF THIS IS ILLEGAL- PLEASE IGNORE MY ADVICE!
OTHERWISE YOU WILL CARRY THE RESPONSIBILITY YOURSELF.
Remember also- even if you do not do anything, sooner or later it will hit them. Everything is just a matter of time- something unpleasant in any relationship will appear and her/his new one is not exclusion.
My genuine advice is live your life and be convinced that it's a matter of time for them to get what they deserve.
If your ex left you and started dating someone else months after that- you must not interfere in any way...
Thank you and please do not criticize me, I was asked for a way to take revenge and just shared a way to do that.