To move a piece, simply click and drag it onto the board, releasing over the desired spot (you do not have to be exact).
To rotate or flip a piece, a variety of methods are available. Choose the one or combination which you feel most comfortable with. There are currently 5 methods:
1) Use the buttons in the lower corners. Doing so will perform the given operation on the selected piece, which is inverted (shown in black rather than white). To select a piece, simply click on it.
2) Use the arrow keys on the keyboard
right-arrow for clockwise rotation
left-arrow for counter clockwise rotation
up-arrow for vertical flip
down-arrow for horizontal flip
3) You can use the keys 'a', 'd', 'w', and 's' to perform the same functions as the left, right, up, and down arrow keys, respectively. You may also change these keys. Simply select "Rotation Keys..." under the OPTIONS menu.
These keys are saved in a preferences file, so you only need to change them once.
4) If you click on a piece but do NOT drag it, then it will rotate or flip. Continued clicking will cycle through all possible orientations of that piece. This minimizes mouse movement and obviates the use of the keyboard.
To cycle through all orientations, clicking first rotates the piece until no more rotates (without repeating) are possible. Then, if flipping results in more orientations, it flips once and repeats the process.
Pressing the space bar has the same effect. It also has precedence -- meaning, if you change one of the rotation keys to the space bar, hitting the space bar will still do this cycling.
5) Shift-click on a piece. Do not let go of the mouse button. As you move the mouse, the program will outline the various orientations of the piece. Let go of the mouse button when you get the orientation you want.
Think of it as moving on a tic-tac-toe board, with the piece as the center square, and the other 8 squares being the 8 different orientations.