How (and when) was it that the verb 'go' began to mean 'say' in common usage?

Solution 1:

Nobody can say when -- or where, or by whom -- this usage came into existence. It's probably been around in one guise or another, in English and its ancestor languages, for thousands of years, because it instantiates a widely used and very important Metaphor Theme. There are a number of concepts converging here.

Go is used because it's part of the Path Metaphor for communication (which in turn is part of the Conduit Metaphor theme).

Go (a Deictic term, semantically related to come, bring, and take) means, initially, to move away from where one currently is located. Maybe directed toward someone else, or maybe just out.

Messages of all sorts go forth from a source. In particular, sounds go forth. Go is often used in children's language to refer to the stylized sounds that common animals make:

• Cows go "moo", dogs go "bow-wow", cats go "meow", ...

So it's a very small step from

• The dog goes "Woof!", and he goes "Ouch!", and I go "What!?"

to

• He goes "I'm not sure we should see each other any more" and I go "What do you mean?"

and in fact, just another small step from there to

• He's like "I'm not sure we should see each other any more" and I'm like "What do you mean?"

Solution 2:

The Oxford English Dictionary’s earliest citation for this use of go is this from ‘The Pickwick Papers’ by Charles Dickens, published in 1836:

He was roused by a loud shouting of the post-boy on the leader. ‘Yo-yo-yo-yo-yoe,’ went the first boy. ‘Yo-yo-yo-yoe!’ went the second.

It may be related to the use of go to describe various sounds, as in, for example, ‘the gong has just gone for dinner’, or ‘the bell has just gone for the end of the lesson’.