|It's not you baby, it's me.|
1. Announce the break up in a public place but in this age a FB status change will do.
2. Do not contact the EX, remove ways to contact you; change your email, cell, address; In worse stalker scenarios consider having a plastic surgery.
3. De-activate your FB account.
4. if you see the Ex, refrain from talking to the breakee.
5. Time heals all wounds, cry as much as you want but it won't change the fact that you don't see a future together.
In all these circumstances, you are not responsible for whatever actions your Ex may take. They will threaten to do suicide, even dramatize one just to win your heart; this shows immaturity on their part
Remember you are doing them a favor by giving them a chance of a better happiness with other people. Realize that there is more to life than being in love, spend time with family and friends.