If you are the "Breaker-Upper"

Say “something” don’t do a disappearing act. Running off and hiding is not going to fix your relationship problems. Disappearing will not cause your partner to get the message and just go away. You are going to have to communicate effectively.
Avoid using “Liquid Courage”. Don’t drink before you break up. You will likely end up saying something you regret later.
“Face” up to it. Unless the person is prone to violence, please, break up in person. No email, no voice mail, no social media.
Keep it short and simple. Have a plan before you engage in the conversation, a short introduction, a short explanation, and a final statement should do it. And then stick to what you’ve decided.
Don’t make it messy. Don’t unload guilt for what you are doing or what you have done. Don’t blame the other person for the mess up of the relationship even if it’s their fault. Don’t say things that will make it worse. The fact is, you are the one who wants to end the relationship so this is about want you want, forget all the other stuff because discussing or arguing over it will only make things worse.

Don’t offer to “Be Friends”. This always ends up being a big mess in the long run and you leave the other person with false hope of reconciliation.
Tie up loose ends later. There’s too much emotion going on during the actual “break up talk”. If you have to move things or settle accounts, set aside a specific time to do it later.

If you have been "dumped"

Don’t ask questions unless you can “handle the truth” (or their version of it). If you are going to freak out or you really don’t want to hear the gory details, don’t ask.
Accept your partner’s statement as their “Final Answer”. If someone got the courage to sit you down and cut you off, they've put some sort of thought into it. If you try to convince them otherwise you’ll just end up being hurt later.