When I was younger I more-or-less assumed that a valve (piston) was a solid rod with holes drilled in it. I never stopped to think about the difficulties of drilling curved passages into a solid tube. Later I figured out that the valves were actually hollow, but how they were made was still a mystery. Now that I have seen the process in person I thought I would share it here. I don't have photos of that experience, but Adams was kind enough to provide me with some photos (not from an Adams euphonium), which may help.

While I have shown only 5 photos below, the whole process is fairly tedious. Some instrument manufacturers choose to purchase the valve sets from specialized companies to save the large amount of time it takes to make them individually.

Step 1:
The process starts with a tube. Most quality valves today are stainless steel; many others are monel. In the past most valves were brass with a nickel plating.

Step 2:
The valve tube is trimmed to length and holes (ports) are drilled. Small tubes are prepared to connect the ports to each other to create the air passages. These are made like many of the short curved pieces in the valve slide assembly. The curves are necessary (and carefully engineered) so the tubes can pass by each other within the confined space.

Step 3:
This photo shows a couple of tubes placed loosely as an example. They are made too long so they can be handled and positioned more easily. At some point top and bottom caps are added as well. Each will have a hole to let air pass through the middle as the piston moves up and down. The top cap here (to the left) also has a hole for the valve stem and an oblong hole for the valve guide. The bottom cup-shaped cap is partly inserted for now.

Step 4:
The short tubes (called "caucades" - or "coquille" or "cociel") are soldered in place and then trimmed. The bottom cap is soldered so that it provides a recess within the outer tube. This allows a place for the top of the valve spring to nest.

Step 5:
Finished valve!

Some manufacturers today us stainless steel on the outer surface, which is better than monel (or the older plated brass valves). Stainless steel is very hard and won't wear significantly even after much use. But it is also structurally stable. There are bound to be some stresses as the newly-bent caucades are fitted and soldered, and it seemed like older valves would sometimes warp slightly over time from that internal stress, causing them to stick. Today warping is much less of an issue. Most sticking in modern valves from good manufacturers is a result of deposits that build up and are not cleaned off thoroughly.

Rotary Valves:
Here is a link to a talented repair man's site, where he is making a rotary valve set from scratch.