This video from Cyber Aware recounts an example of one of many different types of computer hack.
I was amazed some months ago, to nearly get caught myself. A call came in from somebody who knew my name and claimed to be from a Microsoft call centre looking after the security of its operating sytem. They said they had traced illegal activity back to my computer and they wanted to do some checks. Fearing I had been inadvertantly complicit in somebody else's cyber-crime, I nearly succumbed to dowloading the 'diagnostic software' they wanted me to access, but luckily, the combination of how he had initially mis-pronounced my name, plus that fact that I do not have just one but multiple computers running different versions of Microsoft and other operating systems, all using third party security, gave me sufficient doubt to hold back. When he then got defensive after I asked questions about how I could check his credientials and which of my computers he felt was causing the problem, I then new it was a scam - but he very nearly had me. And only yesterday I heard about a friend who, even though they are in the IT business, nearly got caught out by a similar scam, this time by someone claiming to be from Adobe.
What we have to understand these days is that there are thousands of very articulate and educated people around the world, who, merely through the lottery of being bon into poverty, have to work in these criminally operated calls centres, often for a pittance, to survive. All it takes is for one call in several hundred to 'convert' into a cybercrime victim, and their criminal employers are in the money: especially as these call centres are making thousands of such calls every week.
These scams are just a tiny fraction of the wider and growing problem of global cybercrime, and two UK sites to be aware of, to learn of both defensive techniques and what to do to report actual or attempted cybercrime are cyberaware.gov.uk and Action Fraud.