F.W.
I too know just how you feel. I've been a hairstylist for about 7yrs now and I LOVE my job--DON'T GIVE UP! I've always been shy but this job has been the best for that. It's helped me to open up more easily at least with a one on one basis. I had a real hard time in beauty school and for a couple years out of school. I think Dawn had excellent advice (I wish someone would've told me that when I just started!). Try not to worry about convincing people your trust worthy, just assume the trust is already there. If they seem worried just shrug it off, you can make a comment or two like "don't worry your in good hands".
Communication is the key to a good stylist. Just make sure to REALLY listen to what they want and mostly what they DON'T want. Repeat it back to them before you start and through out the hair cut. Tell them you know exactly what they mean, and agree with them when they say what they don't want. If they feel you know exactly what they want and don't want they will feel comforted.
I would start with basic questions like where are you from, what do you do, do you have kids, siblings, ect., just to get a conversation going, but you don't have to talk the whole time. It may seem lame to ask the same questions all the time but who cares, it gets a conversation started and you want to appear relaxed.
Whatever you do don't give up. I have a friend who makes close to $1000 a day doing hair (that makes me want to puke!) so don't let anyone say you can't make money doing hair! It can be one of the most flexible jobs you can ever have, once your clients know and love you they will wait for you if you need time off (I'm on maternity leave right now). And it gets easier and more fun each year you do it, just hang in there!
Sorry about the huge long message, if you ever need any other advice send me a message I'll be happy to help. And don't worry about the state board test, the hardest part is not being so nervous!