Here is how I clamp a piece of stock to the fixture plate for planing. This piece has already been ran over the jointer on the opposing face [bottom side]. I don't often do this procedure, but the stock is too short to run through the planer and I don't mess with hand planes often enough to be any good with them (or own the right one for the job).
On one side I use a "double action edge clamp" which pushes down while pushing forward. That shoves it tight into the clamp on the other end.
On the other end is this clamp I made (on a knee mill, quick and dirty, with a piece of stock that was just knocking about). As you can see there is a screw to clamp it down and a dowel to align it. The slot is long enough to cover 3 holes on the fixture plate, giving it enough travel to fit any length material. The serrated edge is on an angle to help guide the material down to the table.
As you can see, everything falls below the surface to be cut so there are no clamps to avoid although you do have to mind the depth.