He hears from the others, or pieces them together. If I told some stories about Spring 2001, I could probably describe the things that happened, even if I didn’t see them myself.

And why does he tell them to his kids as part of the story about how they met their mother? And why is he giving them so many details about how he was into another woman that he didn’t end up with?

He explains in the pilot that you need to know all these stories to understand how he finally meets the mother. (NOT a spoiler) I won’t give anything away, but as the seasons go on you do get a sense that these are all leading somewhere, and sometimes interwoven (no, not like Lost)

And why does Ted sound so much like Bob Saget as a father? Is that going to happen to me??

That joke was funnier on Family Guy.