I was wondering ... how old are you both (approximately) - are you in high school or college/university?
If you wanted to - you could write her a note saying what your name was, and that you would really like the chance to get to know her a bit - would she like to get together sometime (for lunch, studying, go for coffee/sodas someplace etc). In the note you could also give her your cell phone number if she'd like to text you, and your email address if she'd like to get in touch with you.
Make sure that you take the time to print (instead of write, espeically if your handwriting is messy) your letter, spell things correctly etc - because you want to make a good impression!
If your penmanship is truly illegible then maybe write something out on your computer at home, print it off, and sign your name (then cut it down to a "note size")
Some tips:
Make sure that if her interpreter is with her - that you ALWAYS speak directly to the girl (not her interpreter)... you'll want to stand so that she can see you and the interpreter at the same time. Don't stress about it ... but keep in mind that the girl (lets call her "Jane") will need to have a clear eye-line of the interpreter while also wanting to see you so if you stand a few feet (like 2 big steps) to the side of the interpreter, and a few feet in front, this would be "ideal". Don't sweat it though, just keep it in mind and don't stand directly in front of the interpreter
I'd recommend learning the ASL alphabet which can be found on a number of different websites - my favourite site being
ASLPro.com. The ASLPro website also has a really fantastic ASL dictionary, and phrase guide ... which is very helpful as well.
Don't worry about trying to learn a bunch of things at once though - I'd personally focus right now on just learning the ASL alphabet (when you spell words out using the ASL alphabet it's called "fingerspelling"). Once you know the ASL alphabet it will allow you to ask how to say various things in ASL - which is a great way to get to know each other a bit - just don't make it "20 questions of ASL" constantly because she might think you only are interested in her so she can teach you signs.
Oh - and just an FYI, most people who are hard of hearing or deaf (especially those who use ASL/other Signed Language REALLY dislike the term "hearing impaired" ... so wipe that from your vocabulary if it's something you ever use/think of be aware of that. Typically people who use "hearing impaired" are older people, who do NOT know or use Sign Language and were hearing much of their lives but have slowly lost their hearing over a number of years.
Once you've talked a bit, it's a good idea to ask if she prefers the term "hard of hearing", deaf - or something else (typically the "something else" would be "hearing impaired" but some of us hate that phrase soooo much that it makes us angry/upset to even hear/see it - hence just saying "or something else" and letting HER tell you want she prefers.
Sometimes people use both - for example:
Here I almost always write that I'm "Hoh/Deaf" ...
When I'm talking with people in person, I'll typically say that I'm "Hard of Hearing - but have no hearing at all on my right side AND I a know and use American Sign Language/ ASL ...
If I'm going into a noisy environment in which I know that I will not be able to understand (via listening/hearing) anything that is being said etc - I will say (and sign at the same time) that I am Deaf.
For some people being Hard of Hearing, or Deaf (one or the other) specifically is a major part of their identity - like being Spanish, or American, or Christian, or Muslim, or Jewish etc ... so it's important to listen to how they identify themselves and use whatever term they prefer (Hard of Hearing - abbreviated "Hoh" or Deaf/deaf).
I hope that helps a bit and wasn't toooo much information.
Don't feel overwhelmed - while she may be Hoh or Deaf, she's a person first and foremost