@matejpp - the usual story is that surface water gets very cold due to contact with the air near the Arctic and Antarctic. Cold water is more dense, so it sinks. This pulls in warmer surface water, which comes from nearer to the equator. That in turn pulls cold deep water up near the equator. It goes round and round.
If you want clear diagrams, science journalism is not very good, since many journalists don't understand the science, so they don't know what diagrams would help. Instead, you should read something like Wikipedia. Or you ask someone like me. 🙂
I agree that this is an unsatisfactory state of affairs! But saying "science still lacks communication skills" neglects that there are many people involved: research scientists, professional journalists, freelance science explainers, and so on. Improving the situation requires finding a way to change the motivations for these different groups of people. For example, research scientists are mainly paid to discover new things, and explain those things to other research scientists - not to ordinary people or even journalists.