I guess it depends on the person and the situation you are in.
First off, you want to do it in person; no texting, email, phone call, or letter break-ups because it makes you look like a coward. Now depending on the individual you are dumping, you might want to break-up with them in private; if you know, or suspect, that they might get a little crazy upon being dumped, I suggest you break up in a public area (restaurant, store, park, etc.) so that they can't cause a scene or at least you have people around that could defuse any impending situation.
If the break up is neutral (both of you are just not into each other and want to move on), then just be honest and say that you don't believe that you two should not continue being a couple. Try not to sound smug or arrogant because the break up might seem like your own idea, hence, your fault that you break off the relationship.
If you want to break up because you are interested in someone else (and haven't cheated on your partner), again, go the honesty route. They might be heartbroken, but try to explain to them that you enjoyed being in a relationship with them and are just interested in what someone else might offer in a relationship. Don't list out things that made you choose another partner over your current because then they will make empty promises about being able to do those things or offer more of something for the sole purpose of remaining in the relationship. It's better off to just go your separate ways and that it is your decision and not theirs.
In terms of cheating, you may not want to admit to your partner that you have cheated on them, thus causing the break up. If you want to try and work through any form of cheating, you need to be honest; even if there's no possibility that they will take you back, the fact that you came clean will leave a lasting impression on you. Though you may not end up together, there might still be hope after you have both had some time apart.
If they cheated on you (and you know this to be a fact), then you break up with them stating that you know that they have been unfaithful. Same rules apply here; if they deny it, then you should move on because if you forgive them (or take them back too quickly), they will just be prone to cheat again. If they come clean, then there could be a possibility to salvage the relationship. If not, then you would at least know that they were at least honest to then end, and you can go on knowing that it was not your fault for the break up.