On my concertina, most of the valves were either perished and falling apart (I suspect those were the originals) or they had been clumsily replaced with much thicker leather that wasn't flexible enough (actually, I think it was the same leather that the thumb straps were made from!).
In this photo of the bottom of one of the reed pans, I have already removed all the reeds to make sure I didn't damage them during the valve replacement. The white valves are the original ones. They practically disintegrated as soon as I touched them.
Interestingly you can see in this picture of the top of a reed pan that a certain area of the concertina was much filthier than the rest. I think this is the area that is closest to the player's palms and sleeves:
I cut the old valves off with a sharp skew chisel, then cleaned off the remains of leather and old glue using hot water and cotton buds (AKA Q-tips). This was possible because the original valves were stuck on with hide glue, and the replacements with what I suspect was pine resin glue (it dissolved easily and gave off a strong pine scent). I used as little water as possible and dried it immediately with kitchen paper to avoid warping the boards or softening the glue in any of the other joints. After removing all traces of the old valves I gave the boards a good brushing with an old toothbrush to remove any loose dirt.
Finally I glued on all new valves bought from a concertina spares supplier using hot hide glue.
Each pair of slots is a different length and the valves are sold in several different sizes. Deciding how many of each size to order was rather tricky, and I don't think I got it quite right because I ran out of a couple of sizes and had too many of another. The smallest of the original valves were shorter than the smallest ones sold by the supplier so I cut down a few with a sharp craft knife. Sticking them in exactly the right position without getting excess glue all over the place was quite fiddly; I think I got better at it as I went along.
Time spent replacing the valves: about 8 hours over several evenings.
 The thing that opens and closes to control the flow of air when you press and release a key is called a pad, not a valve.
 On English concertinas the two reeds associated with each key produce the same note, so if you hold a button down and continuously push and pull the bellows you get a bagpipe-like drone (with a slight hiccup each time you change direction). Other types of concertina play different notes on push and pull.
 Carefully laying them out on a marked sheet of cardboard to make sure they all went back in their original positions.