I've spoken to my resident bike expert and in order to fix my chain I need to use a chain tool like this
(which I have) to remove the "busted-up" link and replace it with one of these
(which I don't). I can also use a chain wear tool like this
to tell whether the whole chain is knackered and just needs throwing in the bin.
Off to the bike shop at lunch, I'll let you know how I get on.