Start out by making absolutely sure this is what you want to do. Weigh out the good and the bad from your relationship and decide if you really want to break up with this person or if you are just having a bad arguement.
If you are positive that you want to break up with this person, you will want to try to keep it peaceful. Let this person know that you would like to talk to them about something important. Meet this person somewhere private because if you are in a public place, the other person may get embarassed.
Let this person know why you are breaking up with them, no matter what the reason is. Be honest because this will help the other person understand why you are breaking up with them and will help them be able to change themselves for future relationships if they have a serious problem.
Make sure that you keep the conversation peaceful. Do not start fighting about why you are breaking up because this will only make things worse. If you start to fight, just let the other person know that you have to leave and that you will talk to them about it once you both have calmed down.
Allow the other person to say what they have to say. The other person might try to say things to get you to change your mind, if you feel like they are true about what they are saying, you can give them another chance. If you have your mind set on breaking up with them no matter what, then do so.
Breaking up with someone can be hard but if you are unhappy with your current relationship then you need to do something about it. You only get one life and you need to be happy living it.