How can I approach my loved one about their alcoholism?

Be honest. Be honest and compassionate, yet provide fact based examples of how their drinking is affecting them and you, let them know you love them, yet you may have to make boundries that will no longer support their current behavior, esp if it affects you negatively. It maybe helpful to let them know there is help for there illness and you are wiling to support them in getting help.
Alcoholism. Call for a family meeting to discuss your concerns & enlist support from them to guide your loved one in right direction, then be actively involved in their treatment.
It is difficult. I would try and enlist any and all friends and family at once, and try a unified approach. Maybe, each person could write down and then read out loud during a meeting with your mom, just what her drinking has done in their eyes. The readings should be as non-judgmental as possible, this could be called an intervention. You should also have a plan as to how to get her some help with treatment.