Contacting/asking out a girl I've never met or talked to

I apologize if this is in the wrong sub-forum, I wasnt sure where it goes.

So basically, my friend (lets call her M) is trying to set me up with a friend of hers (we'll call her H). Last week M texted me, saying that she talked to M who is open to talking/hanging out with me. M asked how we should proceed with this, I told her to give H my facebook link/cell number and have her msg/text me. I haven't heard anything from H since. Today M told me that it'll probably be better if I msg H first, to which I agreed.

The problem I'm having is that I don't know what to say. I've never met or talked to H before, and I can't imagine it not being awkward.

I should also mention that we can't just go on a blind date because H and I live in different cities for school (~1 hour drive/train ride) but are from the same hometown, and from what I know we both plan on returning home in a few months.

Has anyone here ever been in this situation? What can I say to make things less awkward initially?

So far I have "Hey, I'm M's friend from school. She mentioned that you might be visiting <city> soon. Would you like to hang out when you're here?"

TL;DR: Never met or seen girl before, messaging her on facebook but don't know what to say.

What you said to say sounds good to me. Clearly mention M in your message to H and maybe ask her to tell you something about her so next time you reply you know more about her and have more to talk about, could include some facts about you to her also.

Your proposal sounds good. You could than ask what she would like to do or suggest something. Maybe get some info from her FB profile about similar interests and you can talk about that.