The first meeting of Superman and Superboy takes place, sort of, in Superboy 47 (March 1956). I've skipped an awful lot of issues, largely because the stories all follow the format of tales I have already discussed. Superboy's series, for the last couple of years, has no recurring villains or new cast members. Most issues contain at least one story in which Lana Lang tries to prove Clark is Superboy. Many have nice art, but nothing that really stands out.
Otto Binder scripts this Swan and Fischetti tale, which I first came across as a kid in a reprint in Super-Team Family. It begins as Clark Kent reads about the future, and then takes a nap. This somewhat signifies that everything that follows is a dream. When he wakes, he flies off, and winds up going through the time barrier, winding up in present day Metropolis, where he encounters his adult self.
Together Superman and Superboy fight crime, and Superboy helps the adult Clark cover his secret identity with Lois Lane. To get him back to his own time, Superman theorizes that if they fly at each other at super-speed, the resulting collision will send Superboy back through the time barrier.
They do this, and Superboy winds up back in Smallville. Dizzy from the collision, he collapses back onto the couch. So was this all a dream, or did it happen?
The presence of Lois Lane in the story makes it very difficult to determine. Either Superboy had a staggeringly prophetic dream, or he really made the time trip. Still, this was never referenced again, so Superman didn't seem to recall these events.