The "black stick," aka "spudger," helps separate the metal bits in the case. In the old PowerBooks and early MacBook Pros, the case is stamped aluminum held together with 3,496 microscopic screws and some invisible and deadly-sharp clamps. The spudger helps you separate the unit at the seams, and it's essential for separating glass from aluminum in all MBP models.
Lacking a spudger, I used a flexible plastic picnic knife. Its soft plastic is non-marring and un-snappable. Worked great; unfortunately most plastic cutlery is too brittle to work. I've heard of folks using credit cards, which are made of the same breed of plastic as my picnic knife but: (a) if you do this, ensure it's a card you have no intention of using again, as the process will tear it up, and (b) the card may be too thick to get the job done.
In any case, work carefully and try to avoid bending any metal out of shape so everything goes back together as gaplessly as it was originally.