Most planers have a minimum thickness of about half an inch or so. If you need to plane some wood to a thickness below this, you can still do so though.

Start out with a piece that is not yet cut to size. Screw it to another piece of thicker wood, putting the screws in in an area of the wood that will be removed when it is cut to size. Once this board is attached to the thicker board, you can plane down to whatever thickness you like.

When putting in the screw, you need to be careful about two things.

One, make sure the screws are countersunk so that the screw heads do not hit the knives. If they hit the knives, you have a big problem. As you make passes through the planer, check the screws every time.

Two, make sure the screws are short enough that they do not come out the side of the board. If they do come out, they will scratch the lower surface of your planer, and the boards will not lie flat.