For 9/11, I was working in an office and one of my colleagues was on the phone to his partner, who was at home watching Sky News and while you could only hear half the conversation, he was clearly trying to signal to us that something big was happening. At first it was thought it was a small plane that had hit one of the towers and that it was probably an accident, then it was realised to be a much larger one, before the second plane then hit and it was now clear it was deliberate.
We didn't have any TVs, but we did have access to the internet in the office, though back in those days there was no video or anything like that, most sites were just text with maybe a tiny photo if you were lucky. We all then spent the next few hours of the day trying to search on various news sites for more info, but quickly noticed that the vast majority of them were down or incredibly slow to connect - it was probably caused by the sheer amount of traffic of others doing exactly the same thing, but of course there were unfounded rumours flying around of maybe terrorists had cut undersea cables or something at the same time.
In the end the best solution was to find news websites based on the other side of the globe where it was still night, such as Australian newspapers or the East Asian version of CNN - they were carrying exactly the same stories and updates as the European and American sites (it was probably being mirrored automatically) but with fewer people browsing them, they would load far quicker.