How do you get better at cheering people up?

If it's a girl, don't bother using logic.
Dance with her, play pattycake, distract her from her sadness with anything interesting like puppy pics. Start adding positive things to say once she's ready to listen.
If it's a guy, then add positive statements and positive facts to the situation. Tell him he's being strong by going through this. Get him involved in some physical activity.

It's what I do, and it typically works. If the person isn't happier after that, it's probably out of your hands and you should just stop bugging them.

Being a natural optimist helps.