Let me try (chem geek can correct me)-
FC/CC
You add the DPD powder to the solution to turn it pink. It's basically a mixture of a bunch of chemicals to adjust the pH, remove any possible interferences from metal ions and, of course, adds indicator dye. The titrant is a ferrous ammonium sulfate solution with a specific concentration.
[EDIT] See JohnT explanation below as it is more detailed. The oxidation-reduction reaction of the dye with chlorine produces the color change. Ferrous ammonium sulfate reduces the colored dye back to clear. This source is a good primer on the dye chemistry [END-EDIT]
To measure CC's, one adds five drops of the R-0003 which is potassium iodide. [EDIT] See
chem geek's post below for proper details[END-EDIT]
pH
This one is pretty standard and you can look it up online. Basically just a color indicator dye (phenol red) for pH. The only trick here is that Taylor adds some special chemicals to neutralize the FC present in the sample in a pH neutral fashion so that the phenol red does not react with chlorine to form chlorphenol red which is a lower pH indicator. The chlorphenol red will turn purple at pool water pH values and give a false high pH color. The cutoff for this reaction is an FC of 10ppm but it's really not pronounced until you get up to 20ppm FC and there are tricks you can play if your FC is between 10-20ppm to make the pH test work.
TA
This is a simple acid-alkalinity neutralization reaction. You add the R-0007 sodium thiosulfate drops to neutralize chlorine so it doesn't interfere with the green dye. You then add the green dye (I'd have to go looking up it's name as I forgot) which remains green at normal pool pH. You then add the R-0009 sulfuric acid drops and count. The sulfuric acid consumes all (well, most) of the alkalinity of the solution and causes the pH to drop. Once the pH hits 4.5 or less, the green indicator turns red. Again, the sulfuric acid drops are a set concentration designed to produce a neutralization of a certain amount of ppm's of calcium carbonate. Therefore TA is reported in units of ppm of CaCO3
CYA
This a reaction of cyanuric acid with melamine to form a hydrogen bonded complex of melamine cyanurate (chem geek has a really cool picture of the structure). The melamine cyanurate is the white precipitate in the solution that causes turbidity and that is the black-dot turbidity method you use. The only twist in the chemistry is that Taylor adds some other chemicals to the melamine drops to make sure that the pH is adjusted to an acidic value (not entirely sure where the pH is but it's probably below 5.0). This is because when you drop the pH, pure CYA is the dominant species and not a lot of chlorinated cyanurates exists. Chlorinated cyanurates do not form the melamine complex as easily.
CH
This one is probably the most complex. You start of first by adding sodium hydroxide drops to the sample. This ensures that any magnesium present turns into Mg(OH)2 which is insoluble in water so as to get rid of the magnesium portion of the waters hardness. You then add the indicator dye which is eriochrome black. It reacts with calcium at the high pH and turns pinkish red. There are probably other additives in the dye solution to help stabilize it and remove interferences from metal ions like Fe and Cu. You then add drops of EDTA (the titrant) which bonds much more strongly to the calcium than the calcium does to the dye. As soon as you strip away all of the calcium from the dye, it turns blue again. This transition can be difficult to see because chlorine can bleach the indicator a little bit and the color transition goes from pinkish-red to a purple color and then to a light blue. Some people mistake that intermediate purple color for the blue end point and get a false low. So adding some drops of EDTA in the beginning can help (you must count them in the total drop count) because it shifts the number of drops to a lower value in the second part of the test protocol. Sometimes counting 30 or 40 or 50 drops can be tedious for some. Adding some EDTA in the beginning can also help remove metal inferences if they are present.
Borates
I have borates in my water but I use the mannitol test procedure outline in
this post. I have no idea what's in the test strips but I found them to be not so accurate when I used them.
Salt (K-1766, in case you're interested)
Salt, well chloride ions (Cl-) really, are measured using the argentometric method. You add potassium chromate to the test sample which turns the water a pale yellow. You then add the titrant (silver nitrate) drop-wise where the silver nitrate reacts with chloride and turns into insoluble silver chloride. This causes the solution to look like curdled milk with a yellow tint. Once all of the chloride ions are reacted with, the next drop of silver nitrate forms silver chromate which is a brick red color. As soon as the test shows a salmon red color (not brick red, that's too far), the test is over. Salt concentration is reported as units of ppm of NaCl. Folks don't often realize this, but adding hydrochloric acid and bleach adds chloride ions to the water. So, even if you never use salt, it is easy for the water to get salty with extensive acid and bleach use.