>Unless you have some kind of very unique skill or you have other offers and the company really, really wants you, how exactly are you supposed to negotiate?

You can play hardball or softball. Hardball works when you have competing offers, and risks your offer being pulled.

Alternatively, you can just ask nicely. I've had luck saying something akin to "hey I'm super excited to join BigCo. I'm just curious, is there any way to move up the comp at all? Just checking, I don't know what the bands are, but if you can come up some, that'd be great. Either way, let me know I don't want to hold anything up, I'm excited to start".

Guess what? Sometimes the hiring manager has the power to come up 5,10,15k if you just ask. I've had luck and other times I've been told "nope" but i've never had anyone be upset.