I didn't go to a birthing class. The nurse tells you what to do when you get ready to push. I am taking our three year old son to a big brother/big sister class Tuesday night.
I started mine early but they were Bradley method which is a 6-10 week course. VERY informative. I think if you are planning a short class you can wait.
I don't think you really need to go to more than one if you pay good attention at the first, I loved my birthing class, it was 8 hours and very informative. My hospital arranged them, as they held them right in the hospital, so ask your doctor. I didn't go until 32 weeks or so, some places fill up faster than others.
You can go to them at any time I'm not sure about more than one though
I'm sure you can,ask you doctors for information in the area,also some leisure centres do them.or find your nearest on the net maybe?