Since rain season is coming, I decided to get some new wiper blades, i've bought the whole assembly (blade and the thing it attaches to), but I am unable to figure out how to remove the thing that the blade attaches to from my blazer, it is the original part.

see what i mean? (http://www.psx-dude.net/external/wiperthingy.jpg)

If you are talking about the wiper arm, there are several ways they were attached to the crank assembly.
Some were pressed on, some had a tab on the side that you need to pull out to release them.