This is from a series of articles by W. H. Davies of Liverpool published in London in The English Mechanic and World of Science
in July and August, 1878, you can also read parts , ,  and  and download a scanned version from Google
though part of part 6 is missing. The piano he describes was old fashioned at the time and uprights haven't been manufactured in this form for a long time, and Mr. Davies services and patterns, as well as the "small work" he recommends, are no longer available so some options might be considered if you follow his directions. I edited and broke it up a little, and reproduced some of the illustrations as vector drawings. The front picture is a drawing of an "English Sticker Upright Action, 1820" reproduced in Alfred Dolge's Pianos and their Makers
Part 5 describes making the action rails and fitting the hammer and damper action parts.
Step 1: The Action Frame
The action frame consists of two end pieces or standards, and two rails - viz., the lever rail and the hammer rest.
The standards are made of 1in. hard wood - generally bay wood - 3in. wide, resting at the bottom on a block 1in. square, and are kept in position by dowels. The top of the treble standard is cut so as to allow it to pass freely under the wrest-pins, and the bass to match; a 3/4in. block 2in. long is then glued to the part leaning against the plank, A, Fig. 1.
The hammer rail is first squared across at the ends of the brasses, this line forming a shoulder to a 2in. tongue at each end, let into the standard, so that a 1/8in. slip placed over them shall be flush at the edge. (See diagram B, Fig. 1).
The tongues are then blackleaded, to ascertain the position of the rail. Put the treble standard in its place, and mark the height of the top bridge pin on it. 4in. below this mark is the position of the centre wire.
Step 2: Mounting the Action Frame
The lever rail is of 1in. pine, 1/4in. longer between the standards than the hammer rail, and giving it that much play. 3/8in. laps are cut at each end, and dovetailed into the standards (C, Fig. 1). The height of this rail is regulated by that of the hopper. For a 2 1/2in. hopper it will be 4 1/4in. from the key bottom to the top of the rail.
An action spring is then screwed outside the treble standard, pressing against the tongue of the hammer rail.
The blocks are glued to the key-bottom, their position indicated by adjusting the hammer butts to their respective strings, the same distance (about 16 1/2in.) being everywhere between the back of the rail and inside the lockboard. A dowel is then put in the top blocks, projecting 3/8in. beyond them; a slight tap at the front of the standards will mark their place on the wrest plank, the holes being bored slightly below.
Step 3: Hammer Shanks and Sticker Levers
To get the length of the hammer stems fit a treble hammer until the nose just clears the bridge pins, and cut the remainder to the same outside measurement.
The key-frame can now be screwed to its place, taking care that its bass key is at the same distance from the standard as the hammer butt. The levers are usually put in to a scale fixed between the standards; but it will, perhaps, be a readier method to first put in the hoppers, carefully spacing them, and set the levers in to match them.
Step 4: Dampers
The damper rail is of the same wood and dimensions as the standards, and 3ft. long. It is centred at the treble end in a "damper rail eye," screwed into the plank, and at the bass, with a "side centre" sunk in the rest. This is a piece of 1in. wood, 2in. deep, fitted between the wrest plank and the projecting front of the end.
At the back of the rail is a square length of 3/4in. pine, on which the dampers are hung (A, Fig. 2). The front is clothed with soft baize.
The height of the rail is ascertained by trying dampers at each end, allowing a working space of 1/2in. between them and the hammers. They are finally hung by the hammer scale.
Step 5: Stickers
To obtain the length of stickers, measure between the levers and the hammer butts, and deduct 1/4in. for thickness of hinge and play of sticker; or if the measurement is required before fitting the action, deduct 8 1/2in. from the space between the top bridge pin and key-bottom.
Step 6: Dampers
To mark for the damper wires : Bend about 1 1/2in. from the bottom or plain end of a wire to a right angle, and screw a button on the top. Place this just under the damper, and mark where the bent end touches the left side of the sticker, Nos. 1 and 60.
The damper stickers are then placed sides up, and a line ruled between these marks. A small hole is then bored 1/4in. from the front, and the wires pushed through and cut close to the side of the sticker, when they will be ready for fixing.
Step 7: Hammer Rest Rail
The hammer rest is a duplicate of the lever rail, bevelled at the inside of the top edge to suit the slant of the hammer, and clothed with soft baize. It is placed so that the hammers when resting on it are from 2in. to 2 1/4in. from the strings.
Step 8: Hoppers
The next task - that of cutting the tops of the hoppers - must be conducted with extreme care, sufficient being taken off to allow the hammers to lie fairly on the rest, without any space or play between the lever and the hopper. The back corner is taken off (A, Fig. 3), so as to let the lever down gradually on the the check, and obviate as much as possible the double blow of the hammer - that bane of single actions - and giving to the tone a most unpleasant twang, as may be readily understood when it is considered that this second contact of the hammer with the string is at a time when the latter is at its fullest vibration.
The hopper checks are cut so as to allow the hammer to fall about 3/8in.* from the strings, and with a slight backward slant (B, Fig. 3). The whole are then blackleaded and burnished.
Step 9: Completing the Action
The damper wires are then adjusted, so that they stand perfectly free between the hammers. The socket rail is slipped over them, and held in its place by the props, which are screwed into the back of the hammer rail. The buttons or damper lifts are put on, leaving a space of a card between them and the dampers.
The rail shade (which is a slip of 1/4in. wood, with a shelf for the dampers to rest on when the rail is raised by the loud pedal) - see diagram, B Fig. 2 - is fastened to the front of the damper rail, and concludes the finishing.
The remaining portion, including the pedaling and fitting the various blocks, &c., is called fly-finishing, the last of all being the regulating and levelling of the keys; but as these directions will apply equally to a check action, I will first explain how this is to be fitted together.
W. H. Davies
(from The English Mechanic and World of Science vol. 27, August 15, 1878, p.566)