How to cheer someone up

I'd say give it some time. The bf's baby tantrum will subside eventually. Keep in contact with her, text her and ask her how she is doing (small talk). Maybe ease her into some activities or events later on. A good convention could do no harm. I personally enjoy tennis and rollerblading as activities, but watching anime with someone or playing video/board games together is a light enjoyable activity as well. She will have to eventually come to the fact that she should not have cheated. Yes, the boyfriend was probably pretty awful, but it doesn't condone cheating. If he is calling her names like that, than he isn't a person I personally would try to work out a relationship with. Simply, break up and move on. 9/10 the other will have learn what led up to the breakup.

WELL HECK CHANGE OF STORY, she asked me to get bubble tea and to see a movie with her this weekend. I'm not sure what to make of this.. xD

Well she is partly to blame for cheating but at the same time if he is an abusive and terrible git then I guess I can understand why - I felt she should have broke it off entirely without the cheating. Right now she needs time to heal and get past this whole ordeal so give her lots of company, be the best friend you can be and let her know she has someone at her side! In time, she'll start smiling and enjoy herself again once she's over it :D

I would say that you give her support when you spend time with her this weekend. Sounds like she'll probably still need it even if she seems fine.

Uhh, talk it over with her. Sounds like she is rushing it. Getting out of a relationship recently and all. Unless you're fine with dating for the sake of dating.

Literally just be there. Talk when she needs it. Sit in silence when she needs it. Every one needs a shoulder to cry on. So all you have to do to help is be there. Time will heal things.

Well if you almost dated then it could mean two things; either she just wants hang out with her friend, chill out and have fun and forget about the rubbish stuff or she's interested in you and might want to pursue something o/ You should totally go for it and see where it leads but it's best to expect the former.