I'm very new to playing the piano and I only had 2 lessons so far. Everytime I practice my hands are sweating all over the keyboard, it's not so bad when I'm practicing on my own, but when I visit my teacher it gets much, much worse and it makes me feel ashamed and insecure. I try to hide it but my concentration and thus my performance is suffering greatly. I don't know if my teacher noticed my sweaty hands (she propably did) but i'm affraid to tell her whats going on because she might be grossed out. In fact I'm considering to quit my lessons because it takes away all the fun and focus. Any tips are highly appreciated.
Sweating is not gross. If you find that it interferes with your play and/or concentration, have a towel handy (like, drape it over your leg or whatever else works well). Don't just unpack it when at your teacher: practice with it at home. Get comfortable placing and using it.
If she asks, just say that your hands sweat a lot when you are nervous. I don't think that's a problem for anybody but yourself anyway, but you show that you are dealing with it.
Square dancers are, by the way, expected to have a towel ready (see this page for example equipment) exactly for the purpose of drying their hands. And in square dance, you are constantly touching your partner rather than a piano.
Make sure that you don't have stale sweat in your clothes and on your body (that is what actually smells bad), and deal with the fresh one by having a towel ready. If you can phase the towel out after a year, so much the better. If not, at least you are not the one leaving a sticky keyboard.
I think that you are just nervous. The simplest thing to do is relax and practice. It doesn't matter if you are not good yet; the teacher isn't going to judge you. She is there to help you get better.
If you keep practicing, you'll get better and you won't be nervous when playing in front of your teacher and thus your hands won't sweat.
Don't give up just yet!
This used to happen to my hands when I first started driving. But I drove more and more and got better at it and now I can drive normally without any sweaty hands.
I'm no doctor but it sounds like you have the medical condition hyperhidrosis. It's made worse by nervousness. Try to avoid spicy foods, relax and put antiperspirant on your hands before you go to your piano lesson.
For other treatments see this link: http://m.wikihow.com/Treat-Sweaty-Hands
Above all else don't be ashamed. Hyperhidrosis affects 1 to 2 percent of the population and it's completely not your fault. If your piano teacher has a problem with your medical condition, find another piano teacher. Playing music is the most important thing. Music will bring you so much joy.
Keep a towel handy. Most of the drummers I work with have a towel that gets used frequently. Flying drumsticks can be lethal; flying fingers less so. It's only a problem if you want to make it one. The teacher will have experienced it before, maybe even of herself. The room may be too hot for you, although it's probably nervousness, as has been said already.Talk to her about it - it's what she's there for. You're paying for advice, let her give it ! Above all, persevere, and it'll get to be less of a problem given time. It is NOT a reason (or excuse) to pack in.