Billy Bob's correct. Left click will turn your cursor into the piece and lieft click a second time will drop it where you want it. Right click to rotate. Also, when you get a piece into the proper spot it kind of clicks into place.
I found it really, really helpful to right click every single inventory item as soon as you picked it up.
WW
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"So then he says it's enough to take aim! What's that supposed to mean?!?"