Fill the shape with all seven pieces. Drag a piece onto the shape and it clicks in where it fits. Tap a piece to turn it. Rotate and Flip act on the last piece you touched, wherever it is lying — and only the parallelogram is ever changed by a flip. Pieces can rest anywhere.
Keys: R rotates, F flips. Without a mouse: Tab to a piece, Enter to take it, arrows to move it, Esc to let go.