I understand completely where you're coming from as I felt exactly the same before we started classes. I've always hated having to get up and do things in front of other people and try to avoid it wherever I can.
The suggestions from the others have been great. We always try to get to our class early to avoid having to walk in when everyone else is there- not only is it good for you not feeling like everyone's eyes are on you but it also makes it easier to control your dog.
The first class we had we did not have to demonstrate anything in front of the class- we were just given time to practise the exercises at the same time.
We've got our last session on Thursday and I have to say that my confidence has increased enormously over the last 8 weeks but I still cringe when I have to get up and show what we can do. I just put all my attention on my boy and try to forget about everyone else.
Whatever you do, don't be embarrassed by your dog's behaviour- all the dogs are there because they or their owners are having difficulties of some kind.
Just go for it and enjoy it as much as you can- it'll be a great bonding experience for you and your pooch.