If you intend to put the raised bed garden on top of lawn, it is best to have a barrier to prevent grass and weeds from growing up into the garden. Landscape cloth is best for placing under a raised bed garden on the lawn.
Plywood would rot and may have chemicals from the glue which could leach into your soil. Plastic would prevent water from penetrating through the raised bed to the soil beneath, causing your soil to stay too wet. Landscape cloth will prevent weeds and grass from growing into the raised bed garden while allowing water to penetrate into the underlying soil. Landscape cloth can be purchased at nurseries, hardware or big box stores.
If you intend to put the raised bed garden on concrete, landscape cloth is also a good idea. It will help retain the soil while allowing water to drain.
If you intend to put the raised bed garden on top of soil that is weed-free, you can break up the surface of the existing soil and then add the soil mixture for the raised bed directly on top. If the existing soil is not weed-free, covering it first with landscape cloth can help prevent weeds from growing through to the garden.