Foam core is the easiest to cut, but it is also a soft material that can be dented easily.
If the design is in a book or magazine, use an opaque projector to make the transfer. If the design is a line drawing, copy it onto a transparency or tracing paper and use an overhead projector to enlarge the image. With either of these methods, the image can be enlarged directly onto the surface that will be cut. If the design is the right size already, use tracing paper behind it to transfer the image to the foam core board. To cut foam core, use a craft knife with a cutting board beneath it.