Essentially anytime someone breaks up with a person they're telling them "You are not (the one)!" or "I believe I'll be happier without you."
Too often people are so concerned about coming off like the "bad guy" when in fact there is no way to dump someone and make them feel good about it! No one wants to hear they're not good enough.
Some people offer the old consolation prize of "instant friendship" which I think is a horrible idea because it gives the ex false hope. Generally exes who become good friends do so after a large gap in time which has allowed both people to move on to happier places in their lives. Feeling uneasy about a breakup means you're human.
There is no need to mention you want to be with someone else because eventually (that's what all breakups mean) whether that happens today, two weeks, or 6 months from now. If you didn't want to be with someone else you'd still be with them. Therefore it's no need to throw additional salt in the wound.
It's best to keep things short and state you believe they deserve to be with someone who will love and value them in a way that you don't or no longer feel. Admit that you're no longer emotionally invested in the relationship and you don't want to rob them of time they could be with someone who is on the same page as them....etc
Refuse to get into a "blame game" or listing a bunch of their "faults" which generally leads to the other person pleading and promising to change. If you've truly made up your mind you're leaving it's because you're not "in love" with them. Therefore don't make them believe if they change a few habits everything will be as it was.
You may want to review some steps I put together a while back.