The URL Problem

Here's my description of the URL problem, as I understand it (i.e. I haven't done any research into the topic, this is the story I tell myself in my head. I'm sure the reality and history is a lot more complex)

Let's imagine we are at the beginning of the internet. There are like 10 computers connected to each other. If I am using one computer, and I want a file on another computer, I need to somehow distinguish which of the other 9 computers I want to access to get the file. There are essentially two problems that need to get resolved
* I need to know which computer the file is on. Maybe I just used the computer recently, so I want to see and remember the name of the computer I was accessing so I can tell my computer at home later which computer I am talking about. Much more commonly (in the modern world at least) I was told the file existed by some external source. Like maybe a friend told me that there's a cool game on his computer that I should try out. In this case my friend needs to somehow communicate to me the information about his computer so I can access it later
* Once I know which computer I am talking about, I need to somehow put some information into my computer and run it through some system that will get me connected to and downloading the right file. Essentially, using the information I have in my head, combined with the information and systems on my computer, I need to reliably (and hopefully without too much effort on my part) get connected to the correct computer.