I do not know your family's situation, but the first thing I would suggest is that you make sure it is all right with your niece's mother for you to begin discussing this topic with her. She may have other plans in place! It sounds like you are very close to your niece, and if you are the major adult female that she relates to, then it would be a good idea to start talking with her about this now.

It is important to present the changes of puberty and menstruation in a calm and clear manner, and in a positive way. You do not want to scare young girls, and you want them to see it as a natural part of growing up.

Fortunately, there are a lot of good books available that can help you get started with it. One of my favorites is The Period Book: Everything You Don't Want to Ask, But Need to Know by Karen Graevelle. This is written for girls, and you can read it together as a way to begin discussing the topic.

Other good books are: What's Happening to my Body Book for Girls (there is one for boys too), by Linda Maderas, and It's Perfectly Normal, by Robie Harris. There are a lot of other books on puberty, and you should visit your local library and scan through a few to see which ones appeal to you.

As far as underarm hair goes, I recommend leaving it alone for as long as possible. In the first year or so of puberty, it is often not very noticeable. For girls with very thick underarm hair, or problems with excessive underarm odor, removing the hair may be helpful. I would not use hair removal products, as they can be very irritating to the skin. It would be preferable to clip the hair or use a gentle razor, with supervision by an adult.