This page was written either before or soon after the millennium and applied to the AC of most cars at that point. The type of compressor used by many cars in the UK has changed drastically since that time so if your model is say 2003 onwards this page may well not apply to your compressor. Some of these tests do not apply to these newer compressors but the page is still worth reading. Horrid noises with Electronically Controlled Compressors will frequently be more serious than with more conventional compressors but don't despair, not all are beyond redemption.
The heading may very well be right but try this first - you may save some money. Turn the AC off and start the car - does it make a noise now? If it does, get someone to switch on the AC whilst you listen carefully - does the noise (A)diminish, (B)stay the same or (C)worsen.
If the noise is very noticeable and doesn't start until the AC is actually switched on then you probably do need a new compressor although it is worth looking to see if the car has a belt tensioner idler pulley as that might just be the source of the noise or maybe allowing the belt to screech. Double check that the noise is not coming from the electric fans on the radiator which frequently start and stop when the AC is turned on and off. It may just also be a damaged clutch boss or face.
Compressors frequently make a little more noise than usual when they are running on a much reduced charge. Sometimes all they need is a full charge of refrigerant. It is also worth saying that my thirty year old Mercedes has a noisy compressor - I've added a little too much oil and I turn the radio up a little but the AC cooled well when I last used it.
If you have (A) above, in other words, the noise get less once the AC is switched on, you could be lucky; the problem is almost certainly a failed compressor pulley bearing - a fairly common fault. If you have read this page in the past you would have read that a failed compressor bearing is usually replaceable. These bearings are becoming more difficult to source as compressors themselves have become much cheaper. You may still be lucky however, it is always worth asking but with most compressor prices falling it is frequently more economical to install a new (or if necessary a secondhand) compressor than to replace the pulley bearing.
If you have (B) above then it is quite likely that the noise is coming from another component, not the airconditioning.
If you have (C) above then you are very likely to need a new compressor.
I should say that recently we have had several enquiries for a new compressor ("my garage told me it was the air conditioning pump") where we quickly found that it was another component which had failed. Some garages have a large blank area concerning aircon and are very happy to suggest it might be that and to offload the problem onto someone else.
new compressor does become necessary many are not too expensive (at least
from an AC specialist) but if your one is one of the expensive ones (the
first law of a certain Mr Sod) then look at a secondhand compressor -
see the page on secondhand parts. If your problem appears to be the pulley
bearing and is gradually getting noisier please do not assume that if
you ignore the noise that you can ignore the problem. Eventually, usually
on a long journey, this bearing will fail completely and the car may have
to be trailered home - very expensive unless you have bought membership
of the AA or Greenflag or similar.