Changing the pivot point and using it to snap to grid I initially learned how to model using Maya, and so I relate everything back to that way of working in 3d space. I want to start modeling in Blender but I am having trouble with some basics...

So in Maya, if I wanted to create a box and snap one its corners to the grid, I would create a box, hit the insert key, snap the pivot point to the corner vertex I want, and then use new pivot point to transform the box to the origin of my grid space.

...but in Blender I can snap the 3d cursor to a corner, and then when I try to move by increments to the origin it won't snap to the origin but instead, it will snap 1 grid unit from the current location.

What is the standard way to do something simple like this? When I search the manual, it seems like it doesn't understand my terminology. Pivot points work in rotation but not in transforming my object, so if I successfully set the 3d cursor to the corner I want and then type in 0,0,0 into the location coordinates, it centers the object on the origin instead of snapping the corner to the origin.
First go to the Edit mode of your Cube and select the vertex you want to snap the pivot to.





Then press ShiftS to open the Snap menu and select Cursor to Selected.  Now you will see the 3D Cursor appear at the vertex.





After that you have to quit the Edit Mode and go to the Object mode of the Cube, then press ShiftCtrlAltC to open Set Origin menu and choose Origin to 3D Cursor.





When thats been done, (still in object mode) press ShiftC  to make the 3D Cursor go back on the grid and while your Cube is selected press ShiftS and choose the second option Selection to Cursor.




Now this will snap your Cube on to the grid.