What are they? An extra 3 hour exam, usually taken after A2s but they can also be taken after ASs. You get either Distinction, Merit or Ungraded and the pass rate is generally around 50% for most subjects, so much lower than for A-levels. They're not available in all subjects and each subject is only offered by one exam board, but they're supposed to be designed on the broad A-level syllabus except with harder questions that actually make you think rather than just test your memory, so it doesn't matter if you do an A-level with one exam board and an AEA with another.
How do you do one? Just ask your exams officer to enter you. If you have to pay yourself, they're about £35 each. They're aimed at the top 10% of A-level candidates, so it's probably best if you got a (preferably high) A at AS in the subject you want to take it in.
Is it worth it? Most students and teachers have never heard of them and most unis don't pay much attention to them because not everyone has the chance to do them, so they probably won't make you look any more impressive, but they're actually quite fun if you love your subject, a challenge and a headstart if you want to study that subject at uni.
Is it a lot of extra work/classes? No. Some schools might run extra lessons for them, but the whole idea of them is that you can't really prepare for them, besides doing past papers.