Most Helpful Guy
She should take the time to grieve properly and to find closure, rather than trying to find distraction in another relationship. Escapism doesn't work as a solution, it is just avoidance. Problems don't tend to just go away with no action, they just wait for you.
What she needs to do with the guy she is seeing is to be honest. Not cold, not rude, but honest. She needs to say to him that she got into a relationship with him when she was in a vulnerable place and at the time if felt right, but as time has gone on she realises that she's not over her ex boyfriend and that she is not ready to be in a relationship. She can say that she is sorry for letting things get this far but that she has to say how she feels because anything less would be dishonest.
Most Helpful Girl
She needs to admit her mistake and be firm, but kind.
"Hey, you're a great person but I screwed up and started dating too soon. There's nothing you could've done differently, I just thought I was over my ex and wasn't. You deserve more and I think we should break up."