What are the special trainers used for spin classes and where can I buy them?

You are talking about clipless pedals.

Spin bikes generally use SPD pedals and cleats for your shoes. You can buy the SPD clips at any bike shop or online. They are shaped like a little arrow and are metal. They are the mountain bike shoe cleats. They are under $20.

You will likely have to buy bike shoes too. I strongly recommend mountain bike shoes because they have tread on them whereas road bike shoes have a slick (sometimes carbon) sole. I have taken a bad slip wearing my old road shoes in spin class and then jumping off the bike and walking the tiled hall to the restroom.

check out these links
Shoes:
http://www.performancebike.com/shop/sub_…

kinda pricey but will last you for years.

Cleats:
http://www.performancebike.com/shop/prof…

The cleats are shown on a black shoe insert. You typically will not use that part. Once you get your gear, take it to a bike shop and have someone put on your clips for you. ( or buy it from your local bike shop)
But if you do it yourself, start with your clip placement exactly in the middle. If knee pressure or pain results, they you can play with repositioning the cleats on the bottom of your shoe.

Just verify with your spin instructor that they use SPD compatible pedals. For a time we had 2 bikes with Look system pedals and that is very different ( and highly unlikely in spin class)