Essential to successful reef keeping is a basic understanding of marine water chemistry and faithful monitoring of tank water chemical parameters.  But don't worry, this is not quite as hard as it might seem. Here we can take you through it step by step...

Salinity:

Salinity is a measure of how much salt (NaCl - sodium chloride) is in the water. The salinity of natural sea water varies by ocean, sea and reef, but is usually near 1.027 specific gravity or ~36 ppt. The two most common instruments to measure salinity are the refractometer and the hydrometer. Reef tank salinity should be maintained between 1.025 and 1.027 s.g. or 34 and 36 ppt. Refractometers are well worth the modest investment. They are easier to read and maintain. Although hydrometers can be accurate if diligently maintained, most aquarists do not have this kind of patience. They quickly lose accuracy when poorly kept and end up having to be frequently calibrated to a refractometer.

pH:

The concept of "pH" is complex and varies depending on the context in which it is discussed. Most simply put, it's a measure of the acidity (or bascicity) of a solution.  Solutions with a pH <7 are called "acidic" while those with a pH >7 are called "basic." The pH of natural sea water varies throughout different marine environments (different oceans and seas), but is almost always basic to some degree or another. Reef tank pH should be maintained between 8.1 and 8.6. pH in a reef tank will fluctuate throughout the day (rising during the day and falling at night). pH test kits come in many different brands and types. All will likely work just fine. "pH pens" (digital pH monitors) are quite helpful, especially to new aquarists.  Considering the fact that many pH test kits sold for the hobby cost anywhere from $7 to $15 dollars for ~20-30 tests, investment in a pH pen (some costing as little as $30) can also be economical. 

Low pH is most often caused by poor aeration, high indoor CO2 levels, and/or low alkalinity levels.  Poor aeration can be remedied with more water flow and turbulence at the surface of the water.  Protein skimmers and overflows might also help with aeration.  If your indoor CO2 levels are high, dosing of limewater (kalkwasser solution) can help.  

Calcium:

Reef tanks need calcium (not just for stony corals but for many soft corals and other reef critters too). Natural sea water has a calcium concentration of 410 to 420 ppm. However, this is a generalization. Calcium levels differ by sea and area of the world and your tanks needs will depend on what type of corals you are keeping. If you are keeping fast growing stony corals (such as Acropora, Montipora, etc.) you should strive to keep your calcium levels at 410 to 420 ppm. However, if you are keeping slow growing stony corals (such as Fungiidae, Faviid, etc.) or soft corals, calcium levels as low as 350 ppm are usually acceptable. Reef tank calcium should be maintained to at least 350 ppm (and at 410 to 420 ppm for tanks with faster growing stony corals). Calcium levels can be too high. High calcium levels bring down alkalinity. It's difficult to have a calcium concentration of 450 ppm or higher while also maintaining sufficiently high alkalinity. Imagine that calcium and alkalinity are on opposite ends of a teeter-totter. When one goes up, the other goes down (and vice versa). You can raise your calcium with CaCl, Ca(OH)2 (aka kalkwasser), or with a calcium reactor. Please see below for information on alkalinity.

Buffers and Alkalinity:

Buffers help protect your aquarium water against sudden changes in pH. The ability of the buffer to prevent sudden changes in pH is called a "buffer capacity." As the term is usually used in the hobby, alkalinity can be thought of as one measure of the buffer capacity of our aquarium water.Chemical compounds called "bicarbonate" (i.e. baking soda) and "carbonate" are the major contributors to alkalinity. They're not the only contributors, but in our tanks, they're by far the most important. They're also what is usually tested for in alkalinity test kits sold in the aquarium hobby. For more information the other contributors to alkalinity and buffer capacity, see Another Look at Chemistry. Reef tank alkalinity should be maintained between 2.5 and 4 meq/L (or 7 and 11 dKH). It's important to note that while alkalinity can *help* your tank resist changes in pH, buffers can be "broken" if pH rises or falls too much too quickly. Therefore it remains important to monitor pH so that it does not fall too fair out of acceptable range. The most common way to raise alkalinity is with baking soda or a commercially sold reef aquarium buffer product.

-------brief guide to adjusting calcium and alkalinity----------

With calcium <300ppm and alkalinity 0 to 6 meq/L (0 to 17 dKH) :
This imbalance is usually caused by over-dosing buffers. To correct this problem, add calcium chloride slowly. It's very important to test the water before and after every dosing. Do NOT use kalk to correct this problem.

With calcium 300-400ppm and alkalinity 1 to 2 meq/L (3 to 6 dKH):
In this situation both your calcium and alkalinity are on the lower side.  Dosing kalk solution and/or some brand of 2-part calcium/buffer solution should solve the problem.

With calcium >450ppm and alkalinity >4 meq/L (>11 dKH):
When both calcium and alkalinity are too high, all you have to do is refrain from adding any calcium or buffer supplements and wait for the problem to correct itself.

With calcium >450ppm and alkalinity <2.5meq/L (<7 dKH):
When calcium levels are too high and alkalinity too low, dose baking soda (if pH is normal) and/or washing soda (if pH is low) to correct the problem.

Note: For 50 gallons of water: 1 teaspoon baking soda will raise alkalinity ~0.4 meq/L (~1.25 dKH). 1 teaspoon of washing soda will raise alkalinity ~0.6 meq/L (~1.75 dKH).

Temperature:

Most corals sold in the aquarium industry are from the Caribbean or Indo-Pacifc. These are warm, tropical reefs. Therefore, unless you know that your reef inhabitants are from colder waters, most reef aquariums should be kept at 78F to 84F.

Interactions

As you will come to experience, pH, calcium and alkalinity interact with each other.As mentioned previously, high alkalinity results in lower calcium levels and vice versa.Because of this, calcium and alkalinity must be measured at the same time and adjusted with respect to each other. Too much or too little of one is often a sign that the other is too low or too high respectively. Low pH can, though is not always, a sign of low alkalinity. It can also be a sign that the water is not being airated adequately. When your tank's water chemistry is not right in some respect, you may have to do some problem solving to figure out 1) what's causing the problem and 2) how to correct it.

When adjusting water chemistry:

1) Go gradual: Don't try to correct an alkalinity level of 1 meq/L or a calcium level of 380 ppm overnight.Alkalinity should not be raised or lowered any faster than ~1meq/L per day and calcium adjusted no more quickly than +/-40 ppm per day. This is especially important since, remember, these two parameters interact with each other. Raising your alkalinity too fast could cause your calcium too plummet too quickly (and vice versa). Whenever you're adjusting alkalinity or calcium, be sure to monitor the other as well.

2) Test diligently: Always test the water before and after you act so that you know what you need to do next (if anything).

3) Observe: Pay attention to any patterns in your water chemistry.For example before fretting over high or low pH, take the time to measure your pH several times over the course of a day or two (test it in the morning, afternoon and night-- before the light comes on, while it's on and after it's off). It is normal for pH to swing in a range as wide as 8.0 to 8.6 over the course of a day (peeking at "noon" and falling at night).