How the hell am I supposed to read A Clockwork Orange?

Read it aloud. You'll discover you CAN understand the words by hearing them in context. Most of them are just an invented slang. Another choice is to watch the movie (Stanley Kubrick did a pretty decent adaptation) and I think you'll start picking it up easier. Be sure to read the book after the movie though, as there are parts in the book not covered in the film. But I think you might catch on quicker if you see it first. By the way, You'll like it. It is pretty incredible!