Illustration from Mansfield, Composition and Presswork For the Student of Printing, 1929

When I picked up my Chandler & Price 8x12 I was also given a galley proof press -- similar to the press illustrated above.  (I'll add a photograph of my press when I dig it out of the back of my garage.)

Instruction on the use of this press (according to Frank S. Henry's Printing for School and Shop, 1917) are:

Straight matter is usually placed on long galleys and proofs are pulled on a galley-press.  This is a framework surmounted by a flat bed, on the sides of which are raised tracks on which rolls a solid iron roller covered with felt.  The frame contains a bin or cupboard for the accommodation of proof-paper.

To obtain a proof on a galley-press the galley containing the type is placed on the flat bed, the type is inked with a brayer, a sheet of paper is placed on the type, and the roller is run over the face of the type.  Owing to the fact that the roller frequently squeezes the type into the paper, the paper is apt to slip over the face of the type and smear the proof.  This can be avoided by holding the paper tightly against the roller and rolling them together over the face of the type.  Care should be taken to see that the galley has not too thick a bottom, for if the impression is too heavy there is no way of altering it.  If the impression is too light, a thin cardboard or a sheet or two of manila paper under the galley will correct the fault.  The press is intended only for galleys of type, not for small jobs.