To bracket with shutter (which is what you want to do):
1) Put it in Manual, set your aperture according to how you want your depth of field, set your shutter to what your metering tells you
2) Set shutter a stop brighter than neutral, shoot
3) Set shutter to neutral, shoot
4) Set shutter a stop darker than than neutral, shoot
What I define as "neutral" is what not necessarily 0.0 EV, but whatever you might consider neutral for your camera and/or the scene. Most of the time, I have my D40 set to -0.7 EV.
Point camera at scene in auto mode, it will give you 2 readings aperture and shutter, take the shot, switch to manual mode, set the same aperture then do two shots one with the next higher shutter speed and one with the next slower shutter speed. H
The only problem with that is that it's an extra few seconds diddling around with controls. Keep in mind that you'll want to do this quickly, yet gently, so that you get the composition and subject as identical as possible.
that button is to adjust the aperture, correct?
Yes, in Manual. In other program modes, it is the button for exposure compensation.