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Even during the breaking up, try not to console them or make them feel better. I don't mean be a jackass. Other comments have covered the overall approach very well already. I just mean trying to help them feel better about it is really just for you. They're going to and are allowed to process it however they're going to, and you give up a right to try to be a part of their healing when you break it off.
Be kind during, give them space if you actually want to remain friends after, and let them process and heal how they will.
As I've gotten older I've actually preferred to be broken up with over being the one breaking it off. It's hard to do that to someone you care about but isn't a good fit for whatever reason. When it's broken off with me I can say so be it and start moving on and not have to hurt another person in the process.
I'd much prefer to be broken up with than be the one to break it. It is hard to see how other people handle emotions differently than you would, and sometimes I wonder why people react the way they do.
Thanks for the answer