I have a plane in blender with a image texture node, connected to a RGB to black and white node connected to a multiplier before being connected to the displacement of the Material Output node. There appears to be some shadowing on the plane but it is only this that changes when I change the multiplier, the plane while viewed from the side rendered is still totally flat. Do I need to bake this in some way? Or have I totally misunderstood how displacement textures are supposed to work?
Change the displacement type found in the Properties window under Object Data from (the default) Bump to True.
Note that this is an experimental feature and you must change the feature set from Supported to Experimental in Properties > Render Settings > Render.
True Displacement: Mesh vertices will be displaced before rendering, modifying the actual mesh. This gives the best quality results, if the mesh is finely subdivided. As a result this method is also the most memory intensive.
Bump Mapping: When executing the surface shader, a modified surface normal is used instead of the true normal. This is a quick alternative to true displacement, but only an approximation. Surface silhouettes will not be accurate and there will be no self shadowing of the displacement.
By default, using the 'Displacement' plug in the Node Editor does not truly displace the mesh, but "bump maps" it instead, which essentially means that it approximates the appearance of displacement without actually displacing it. In order to actually displace the mesh, you are going to have to use a different techique.
Although there are a variety of ways to do this, the standard way to displace a mesh, instead of using node 'Displacement', is to use the Displace modifier. To apply your node setup to the Displace modifer, choose a texture in the modifier panel, then select that texture and edit using the Node Editor.