2000 gals is a lot for a couple of 1" tabs to chlorinate. I put one to two tablets into a 350-gallon hot tub and sometimes even that isn't enough to maintain proper chlorination. I'd be looking at one to two 3" tablets for pretty much anything you'd call a "pool".
The short answer to your question is, yes, you want to put a "start-up" dose of chlorinating agent into your pool to get it to the proper chlorine level (or slightly higher); from there, a "maintenance" dose of chlorine such as from the tablets will keep the proper level.
The longer answer is that there is more to conditioning a pool than chlorinating it. The chemistry beneath the surface has been the subject of many a doctoral dissertation, but the products available commercially, while not idiot-proof, are hard to get wrong if you follow the instructions. The steps you follow, in order, are:
Balance pH - The water should generally be slightly higher pH than neutral, generally between 7.2 and 7.6. Too low and you risk an acidic environment which can damage metal parts like your pump. Too high and the water will cause ichy, dry skin (or in the extreme, chemical burns) because the high pH breaks down natural body oils (a process called saponification, which is the same as is used to make soap).
The typical "pH Down" (acidifying) product for home use is sodium bisulfate, NaHSO4, which is an "acid salt" based on a partially-neutralized strong acid (sulfuric), which works as a weak acid in water. This product, in powder form, is safer to use and store than liquid muriatic (hydrochloric) acid, HCl, which is commonly used in large public pools where you don't have time to mess around with dissolving several pounds of a powdered product. Muriatic acid also reduces total alkalinity (useful if your water comes from an aquifer, less so if you're already fighting soft water from a marsh or river). "pH Up" is typically a weak base, such as sodium carbonate or sodium bicarbonate (baking soda), while lye (sodium hydroxide) is used commercially; sodium bicarbonate also increases total alkalinity.
Work in small amounts and let the chemical dissolve and mix thoroughly in the water as you go. Also, never pour acidifying products directly into your skimmer; the concentration needed to balance a full pool will make the water in the circulation loop highly acidic for long enough to cause serious damage to your pump's impeller and other circulation parts. Alkaline products, not so much; the alkali metal cation already attached to the hydroxide or carbonate anion is more attractive than the transition metals of the impeller, heater etc, so these are typically skimmer-safe. Just don't ever put any balancing product (any maintenance product, really) in the water while anyone's in it.
Buffer - You need the right amount of alkali metal in the water, and of a "chlorine buffer". Basically, you want the water "hard", but not so hard that you have to deal with scaling on a regular basis. Chloride salts, like calcium and magnesium chloride, both add some chlorine to the water, and more importantly provide a pH buffer with the alkali metal, giving acidic compounds (like many chlorinating compounds) something to dissolve besides the metal parts in your pump. Sodium bicarbonate (baking soda), in addition to increasing pH, also increases total alkalinity. Too little alkalinity can cause large swings in pH as chlorinating agent is added and then burns off. Too much alkalinity raises pH, reduces the amount of "free" chlorine that can actually do the disinfecting work, and causes cloudy water, scaling, and itchy dry skin.
As for the chlorine buffer (often called a "stabilizer"), cyanuric acid is generally used. Cyanuric acid reacts with chlorine to form stable "chlorinated cyanurates", which are good disinfecting agents and also prevent the chlorine being lost from the water as gaseous chloramines. These products are generally skimmer-safe; you may avoid putting straight cyanuric acid in the skimmer, but cyanuric acid is a weaker acid than hydrochloric (enough that it has a negligible net effect on pH when added to properly-balanced water). Watch the amount of cyanuric acid you put in; unlike the chlorine compounds, cyanuric acid is ridiculously stable and will not "boil off" (which is why it's used), and won't readily react with the alkalinity in the water, so too much of it cannot be negated by adding something else; the only way to get rid of it is a partial drain and refill to dilute it.
Shock - The general goal of "shocking" the pool is to temporarily superchlorinate it, which kills bacteria and algae; the normal level of chlorination is a deterrent to bacterial growth, but certain nasties are chlorine-resistant, and the amount needed to guarantee the water is sanitary is a bit much for humans (and their swimsuits). Shock is also designed to "burn off" relatively quickly, carrying the organic byproducts of bacterial destruction with them (that "chlorine smell" of a pool is the smell of organic chloramines evaporating, the result of the shock doing its job to clean the water). The end result should be clear, blue water, free of chloramines which turn the water green, and with a free chlorine level (unattached Cl- ions) of between 3-5ppm.
A variety of actual chemicals are used to shock water; sodium hypochlorite (chlorine bleach) and the related calcium hypochlorite are definitely effective, but tend to have detrimental effects on swimmers' skin, hair and swimsuits, and the distinctive "bleach smell" which is good for laundry, bad for swimming. Many powdered shocks have more complex, tailored chlorinating chemicals that act as disinfectants but not bleaches. Many powdered shock compounds also include a "clarifier", which is a substance that causes small particles (which normally have a small negative charge and repel each other) to group together into bigger particles, so they won't remain suspended in the water and can get caught in the filter. Most shocks also include a dedicated algaecide (see below). Shock is almost always skimmer-safe, but chlorinating agents can lower pH if there is an insufficient amount of an alkali buffer.
Once these three steps are performed, dip a test strip and verify that the water has the proper pH, hardness/alkalinity, total chlorine, and free chlorine. If there is too much chlorine and slightly low pH immediately after adding the shock, that's normal; within a couple hours of sunlight the chlorine level should go down to swimmable levels (and the pH should go up as the chlorine ions are removed). If there's WAY too much you added too much shock; make sure the pH isn't too acidic (still above 7; add some baking soda to counteract the acidity if it's too low, and you'll need to keep an eye on the pH balance) and keep people out of the water until free chlorine comes back down to 3-5ppm. There are "shock and swim" products designed to be swim-safe very soon after adding them; these usually use a "self-buffering" chlorinating chemical that reduces pH swings and the severity of the free chlorine spike, to prevent harmful levels of free chlorine while still being enough to "shock" the water free of contaminants.
Chlorinate - Most of the chlorine in your water at any given time should be added by shocking it. However, shock is generally short-lived and the amount of chlorine in the water will rapidly decrease after shock is added. To combat the loss of chlorine and stabilize the total/free chlorine levels, you use chlorine tablets, which dissolve in a time-release manner to add chlorine back into the system at a relatively constant rate. The number/size of chlorine tablets you need depends on the size of your pool, whether it normally stays covered or open, how much cyanuric acid you have, whether you have a dispenser (which further controls the amount of chlorine released into the pool by controlling the flow of water into the dispenser chamber with the dissolving tablets) etc. Like I said, chlorine tablets are not a replacement for shock and vice-versa. A chlorine tablet in the skimmer won't harm anything, but it may cause the tablet to dissolve too quickly, over-chlorinating the pool.
Algaecide - Included in many shock products and also available separately, the typical algaecide is a quaternary sanitizer that is more effective against multi-cellular algaes than chlorine alone, and is generally less harmful to humans (quat sanitizers are food-safe where bleach is not). If the test strip says the water's good, but the pool walls feel slimy, a dose of algaecide is usually the answer. Too much algaecide can cause a loss of chlorine (quaternary sanitizers are based on ammonia, and those chloramine gases I mentioned earlier that cause "burn-off" are chlorinated ammonium compounds) and can also mess with pH (remove chlorine from a balanced mixture, and the alkali metals left behind will react with the water itself to form hydroxides, raising pH). Despite this, algaecide is generally skimmer-safe.
Best Answer
CYA can be higher than 20-40 without any problems. I'd say it only become a problem when you start going over 100. It's true that you can't get rid of it without partially draining your pool, though.
Your CYA should be ~40ppm, so once you figure out what it is, adjust it as necessary, partially draining and refilling the pool to lower it, or adding CYA to increase it. (I haven't used a taylor test kit in probably 10 years :S Are you sure it's really 300 ppm? If so, I'd pretty much drain the entire pool... lol.) CYA keeps the chlorine from evaporating off and is very important, but having too much CYA makes the chlorine ineffective. Once you get your pool to ~40 ppm CYA, add bleach at night (to help prevent evaporation) with the pump running.
If you find that you are still unable to hold FC even with a good amount of CYA, then you have "chlorine lock," which is a situation where, when you add chlorine, it combines with something (typically ammonia or urea, created typically by not maintaining proper chemistry, at which point your chlorine evaporates, followed by microorganisms eating your CYA, turning it into ammonia and urea) very quickly. Some people out there kick and scream when they hear the words "chlorine lock," even though they do not question that there are situations in which free chlorine will be gobbled up very quickly. They hate the term because they hate the pool chemical industry / pool maintenance companies, but pretty much everyone agrees on the solution, and it's very simple: you need to add a large amount of chlorine into your pool, whether it be chlorine shock (that does not contain CYA) or liquid chlorine bleach. When you have chlorine lock (i.e. an ammonia/urea problem,) adding a half-gallon of bleach is like attacking a ten-acre fire with a garden hose. It's the right idea, but not on the correct scale.
Here's how to fix the problem:
1 diluted tsp / 1 gal pool water = 15,500 diluted tsp / 15,500 gal pool water15,500 diluted tsp / 768 tsp/gal = 20 diluted gal20 diluted gal = 5 full-strength galUse 4.5 instead of 5 to be on the safe side. This likely won't be quite enough, so if you find that your pool is still unable to hold any FC, add 1/4th of a gallon of bleach each night until it starts holding some FC.