Girlfriend's ex boyfriend dies?

Recently my girlfriends ex ped and she is understandably sad. I have recently gotten sober (for life) and have no coping skills other than drugs and alcohol which to rely upon so my question is how should I approach this situation? I am an admittedly jealous guy so I don't exactly like her freaking out but I understand that there is obviously going to be a period of grief. I want to know how to comfort her without depressing her even more or pissing her off.