I've never accessed the dark web, not do I have any desire to do so.
As Hans notes, seeking that kind of advice is a bit like seeking advice on how to deal drugs, or write computer viruses.
Not the kind of information that you want to give out on a family website.
The dark web is just that. Dark. Hidden. By design.
People who want to do things without risk of being identified use it. That very often means criminals, but also those who are concerned about the proliferation of private data and want to keep their identity and activities secret.
Standard internet technology links many computers together.
When accessing a regular website such as TheAnswerBank.co.uk, your computer looks up the address in a public look-up table (called DNS), and discovers that the 'address' of TheAnswerBank is something like 64.237.61.68
When you type the address into your browser, all kinds of information leaks out to various people and organisations.
Take a look at this link, for example
http://mybrowserinfo.com/
If people want to put a lot of that data together, they can find out huge amounts of information about the user and his or her activities, where the user has been; what sites they looked at and so on.
Those who use the Dark Web use specific browser software that hides this kind of information, and furthermore uses specific software to hide the addresses of the source and the destination of each web request by jumping through a series of hops, each one of which should be untraceable. Make five or six, or 1000 (or 1000,000) such hops and the request cannot be traced. Hence the Onion analogy
Add to that end-to-end encryption and other security systems, and the dark web becomes a place where residents can do anything they want, with no come-back and no fear of identification. I leave to to your imagination.
The OP said they keep hearing about the dark Web in the context of crime dramas or crime reports on the news.
That might give a clue as to the kinds of activities you might find there.