Muriatic acid is used to lower your pH. Only use this when you need to, and do be very careful when using it. Wear personal protective equipment such as goggles and gloves. The vapors are very strong and can harm your lungs, so stand up wind when you pour directly from the bottle.
use a 5 gallon bucket half filled with water (or as much as you can lift), pour the muriatic acid into the water and stir with a plastic spoon (no metal spoons). Then pour the bucket slowly in front of your return.
Cyanuric acid is, as Oly noted above, often called stabilizer. Consider this sunscreen for your chlorine. Without it you will lose all of your chlorine every day. It helps keep the chlorine stabilized so that it doesn't all disappear. You will only need to add this if your CYA test is too low, but let's check that when you get your kit. Also, you should only need to add it once, for the moment. It is far less dangerous to handle than the muriatic acid. It is commonly sold as a powder which is cheaper than liquid, and you will use a sock (from your sock drawer) tied off at the opening with a string to hang it in the water (away from the wall) and soak it so that it dissolves. We squish the sock every half hour or so to help it disperse. Once it's in the water, it is there and doesn't normally decrease (unless you backwash a lot of water out).
Chlorine and liquid shock are the same thing. When we say chlorine, it is referring to all forms of chlorine which includes the liquid shock, bleach, chlorinating liquid, trichlor (tablets), dichlor (powdered shock products), and cal-hypo (another powdered shock product).
As to what to do with the tablets you have... I would save them for the moment. You may have to be away for a day or so sometime, or you might want to use them to increase your CYA a little. Note, they will also lower your pH. For regular maintenance though, don't use them. Use liquid chlorine (shock) or bleach for regular maintenance after your CYA level is set manually by you.
Happy shopping!
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