How do I center a 2x2 plate on a 3x3 plate?
I saw this technique in LEGO's Disney Castle for offsetting parts of a column by half of a stud.  You can see the column on the left in this picture is shifting half a stud above a 3x3 plate:



Of course you can do it too!  Here is the process:


Take your 3x3 base plate and stick 1x1 "dots" between each of the studs.  The "dots" are LEGO part 4073 which BrickLink calls "Plate, Round 1 x 1 Straight Side".  So you end up with 4 dots on your 3x3 base.  I didn't have a 3x3 handy so I start with a 4x4 to demonstrate:


Those dots form a new layer that is half of a stud off from the base plate (3x3 for the OP, 4x4 in the pictures).  So you can just stick your next plate on it. (2x2 for the OP, 2x3 in the pictures)



Addendum

A friend wanted to verify this and so we get to see the parts originally requested: