Is it like Portal 2 where you can only activate it once? Or does it just use Steam, but you can still sell it used once you're done?

Are you talking PC?
On PC a steam game cannot be sold on. Steam are currently working on some sort of buyback system that will give you credit to use in the steam store if you no longer want a game, but this is far from being implemented.
If you buy it for PC and activate it on steam it is yours for life. I don't know if there is an install limit or any extra DRM (I doubt it but I can't check the page to tell since I'm in the UK)

If you're talking Xbox or PS3 then I have absolutely no idea.

You can install steam on as many machines as you want, you just cant run the steam client (which is required to run the game) in online mode on more than one machine at the same time. You can install Steamworks games (like Brink) on all those machines.

So if you're logged into steam on your desktop, and you log in on your laptop, the desktop will get logged off. But beyond that if you have 10 PCs you can install it on all 10, for example.

Why would you want to run the client online? Well, you cant play online unless the steam client is in online mode, afaik. Also, Steam Cloud will sync your savegame for Brink between your machines. Handy.