How does HQ work in Black Ops

I believe you are referring to Dead Ops Arcade. Here's an explanation I found of how to access it.

Accessing it isn't just a matter of finishing the game. You've got to bust your way out of the main menu screen, then work your way around to a terminal and type in the correct commands to boot the game.

While in the menu look down (using the right analogue stick, presumably) at your hands and mash the triggers to wriggle your hands until they come free.

You'll stand up and be given the freedom to roam. Go to the terminal, access it and enter CD, then DOA. Bam - giant machine guns, flame throwers and rocket-firing bats are yours for the shooting.

Spawning in Black-ops tries to place you next to a 'passive team-mate'. Essentially it will find a player on your team that is currently not in battle and near one of the designated spawn points.

If both of those are satisfied it will spawn you there. You can see how this idea could be very very flawed (Example: an enemy is about to start firing at the 'passive team-mate' and your respawned right next to him... Easy double kill).

If there are no 'passive team-mates' it will attempt to spawn you in a "safe spot" away from other players.

In maps like Nuke Town its just not big enough for this mechanic to work, hence it feels like you spawn in the same place everytime (I believe theres only 2 spawn locations in NukeTown) where as a larger map with more spawn locations can actually begin utilizing the placement algorithm.

Hope this helps