Boy after several of these types of incidents, this really creates the impression that a hacker can just arbitrarily break into anyone's e-mail account that he wants to. (This particular article mentions a hack of someone's personal Yahoo e-mail account, and another person's Gmail account, plus their DNC work e-mail accounts)

This seems like magic; I mean what methods are they using? Is it mostly phishing, if phishing is really that effective? Scratchin my head here as to how they can just grab any account they want.

Ah, I think I found an answer:

https://www.crowdstrike.com/blog/bears-midst-intrusion-democ...

And yep it appears they started with primarily phishing.

Targeted (spear-)fishing campaigns can be pretty effective, especially combined with unsecured, generally available email/message systems.