Help with Twitter

I want to use Twitter to establish communication between different classes. So for example, all social studies classes studying a particular topic could twitter during class. I"m betting that there's a way to do this but I don't know how.

Would somebody please explain to me how to set this up.

(I've actually recently started a social network group for Jewish educators, jedweb.ning.com. I simply want classes that are studying Jewish studies to be able to twitter. Later we could definitely make these groups more precise. But I don't know how to set them up to begin with.)

Any help would be much appreciated.

Thanks.