Every brass player, at some point, has to take their instrument apart to clean it. When they do, they will notice the parts of the horn that aren't like the rest. The majority of the valve is made of a metal cylinder with holes through it, and a stem area of a smaller diameter. But, there are parts that go with the valve that matter just as much, and they serve very important purposes.
Along with the valve, there is a spring. It's a coiled spring, either inside or outside of the first smaller section of the valve. This is what makes the valve go back up when you take your finger off of the top. This part is pretty self explanatory, but there are a few things younger players need to keep in mind. First, the spring should be left alone. Second, THE SPRING SHOULD BE LEFT ALONE. Not fussing with it whatsoever will mean this spring will be the longest lasting part of the instrument, as far as things that would need replacing. Stretching it, pulling on it, even squishing it down apart from normal use will decrease it's lifespan. Removing it for cleaning should involve as little force as possible, and reinstall it as soon as things are clean. Period
Next, the valve guide. This is a a little piece of hard material used to keep the valve from spinning in the valve cylinder. Without it, the ports in the valve (the holes) won't line up with the slides anymore, and air won't go through the horn. When removing the springs, the valve guides will usually come out at the same time. The only hard part about that is making sure they go back in the same direction, so that the valve faces the right way, and the problem with the valve spinning doesn't show up.
There is a choice that some instruments can make here, and it pertains to what the guide is made of. There are really 2 choices at this point: Metal or Plastic. To some degree, it is a personal preference. The metal ones will last a lot longer, and the plastic tends to be quieter. Any other difference anyone tells you is subjective and a bit of placebo on their part.
Next, and very importantly, are the bumpers. The first set of these is on the skinny part of the valve stem, right under the top cap. The second set is either on a ring on top of the valve cap, or on the underside of the finger button, sometimes even both. It serves two purposes. The first is that acts as a silencer for when the valve travels up, being a soft cushion for the two surfaces to impact. Without it, the metal of the valve and the metal of the cap would hit, causing a clacking noise every time the valve moves up or down.
The second purpose, and possibly more important, is one of alignment. This bumper helps to ensure that the ports in the valves line up as perfectly as possible with the holes in the valve casing, meaning no air restriction from the valves to the slides. Air restrictions mean working harder, and with less of a good tone. I will say that this comes with a small disclaimer. There can be a small fudge factor in how well the alignment is before it starts to affect anything. Over time, they will compress, meaning that depending on how long it will be before I see the instrument again for maintenance (yes, I do ask new clients) I sometimes install slightly thicker bumpers than I need. That way, in a few months, the spacers will compress to where they need to be so they can stay there for years.
With bumpers, there are a few materials out there. From felt, to cork, to soft rubber, and probably a few others I don't know about yet. The firmer the material, the less it will move over time, but the more noise they may make. Bach has, for many years now, used a rubber ring in the valve caps for their bumpers, and the valves are known to be a little noisier than other horns for this reason. Most repair tech will carry a supply of any of them, and can accommodate you on anything you ask.
With any of these materials, however, the important thing is to leave them alone as much as possible. The more they are moved around, messed with, or affected in any way, the quicker they will deteriorate. Replacing these, regardless of how easy it seems, is better left to a professional. It saves you a trip to the repair tech to figure out why it doesn't play as well as it used to.