Normally, when you have a template loaded and ready to paste, it will rotate on the Z (Length/Width) axis of your build without the need to hold a key. Holding the control key will make it rotate on the Y (Width/Height) axis.
Preparation at the "copy" stage may be needed with your templates since 99% of the time, they are offset in such a way why you can't paste them in the desired location without first building out to that area with extra blocks and then deleting them afterward.
Definitely not an intuitive process but it gets easier over time.