I'm trying to customize the administration toolbar in Drupal 7 but I don't know how to do it. I'd like to add custom links (e.g node/add/[content-type]) and links that are only available for specific users.
Use the shortcut module that's in core, that's what it's for. The Toolbar wasn't designed to add custom links because the shortcut bar was (from what I understand). Ironically the Drupal 6 backport module of the module does have this feature.
Take a look at the Quickbar module.This is a simple administration toolbar. It allows you to take any menu and assign it to a role. This menu will be displayed at the top of your page as an administration toolbar.
You could also look at the Manager module. It includes the Manager's Bar. An admin-bar designed for users that aren't familiar with Drupal. It is like the default "Navigation" menu, when we cut off everything that doesn't matter to this users, and it looks like some known admin-bar-modules, like Admin Menu, but a lot more simple.