Connect each blue box to the black box to the black box, by rotating each box and pipe into the proper position.
Each blue box has one connection, while each pipe may have between one and three connections. Connect an element to a pipe by making a connection. Each box and pipe, including the central black box, can be rotated by tapping on it. If blue box is connected to the central black box, it will light up. View how many boxes you have connected on the bottom status bar. When all the blue boxes have been connected, you have one, a gray wave will emanate from the center, and the bottom status bar will read "COMPLETED!".
To increase the difficulty, make the grid larger and/or let connections wrap around the screen by selecting an option in Settings on the toolbar. You can also define a "Custom Game," to set any size grid with or without wrapping. By default every level has unique solution, though if you want the uncertainty (or certainty that you will go insane) you can disable this in the Custom Game Dialog.
If you are playing a level that has wrapping, a connection can be made between the left and right side of the screen and top or bottom of the screen. This has the effect of making the game much more challenging as you have to keep track of where things cross.