How are Chinese keyboards designed?

I'm puzzled by how a Chinese keyboard can work - with so many thousands of characters, surely every keyboard would have to be enormous to work (unless that's why they say people don't use the internet as much in China...). Please could someone explain.

Another thing I was wondering is how do you use a Western keyboard to get Chinese characters - I've not got on to learning characters myself yet, but it would be interesting to know how.