You want the putter face to be perfectly square, or perpendicular, to the target line, which is the intended path of ball travel.
As for your body, you want your torso, shoulders, legs, feet and forearms to remain in line with the target line. If your shoulders are turned left or right of the target line, or if one foot is ahead of the other in relation to the target line, you are setting yourself up for failure.
Ironically, one facet of alignment that is easy to overlook is eye alignment. You can have everything else in line with the target, but if your head is slightly cocked to the left or right when you address the ball, your eyes may sabotage your stroke.
In his excellent instructional DVD called The Putting Arc Stroke, teaching professional and Putting Arc co-inventor V.J. Trolio offers a simple tip for checking your eye alignment.
Find an old compact disc with a clear reflective surface, then draw a straight line through the middle of it with a Sharpie pen. Place the CD on the ground with the Sharpie line pointing directly toward a chosen target, and address the hole in center of the disc as you would your ball. When you do this, you will see your face reflected in the CD, and you will be able easily to confirm that your eyes are in line, or out of line, with the target line.
For a proper setup, Trolio also recommends that your eyes be either directly over the ball—in which case, the line on the CD will intersect both eyes in your reflection—or an even inch or two inside the ball, where they will be reflected in the bottom half of the CD closest to your feet.
P.S. This alignment drill is easily performed on your living room carpet, but remember to wear shoes when practicing your putting indoors, as you want to replicate the height at which you normally putt.