There is no one right way of getting started with a reef aquarium. There are so many different types of approaches such as the popular Berlin method and even more natural methods without the use of a skimmer. I will only recommend from my personal experiences and from what I discern as credible information from my research on the Internet and from the books I have read on reef aquariums. There are so many excellent articles on this subject so I will not go into detail but instead provide some of the basics.
The method I use for my aquarium is similar to the Berlin method. The three most important aspects of this method are the following:
1) Live rock (about 1 1/2 to 2 pounds per gallon)
2) Random water movement and oxygen exchange
3) Bright lighting
Live rocks sold in the US, most of the time, are from Fiji, Tonga, and the Marshall Islands. The rock is teeming with all kinds of life, hence the name "live rock". Live rock is almost a necessity in the reef aquarium because of the tremendous capacities for natural biological filtration. Make sure you get the most porous rock that you can find because you will want the most surface area you can get. This means getting rocks with many holes and branches with lots of "character".
Avoid getting items such as base rock which is rounded and bulky without much holes. This uninteresting rock usually will be limited to biological filtration. Also, avoid getting rock that is not fully cured, unless it is fresh and doesn't need to be cured, as this will lead to a longer time for cycling the tank. Smell the rock if you can and try to sniff for a fresh "sea" smell. Any foul odors (sulfurous) will mean that it is not cured and things living on the rock are dying. Some of the more premium rocks will feature purple to orange encrusted coraline algae, macro algae, and many hidden beneficial worms and invertebrates, maybe, if you are lucky, small corals.
Random Water Movement and Oxygen Exchange
Reef aquarists know the importance about having strong circulation or "flow" in the aquarium. The powerful and random, sometimes chaotic, flow of the sea is what many reef aquarists try to mimic in their little enclosed tank systems. It doesn't matter if you have a 10 gallon or 500 gallon tank, you cannot compare it to the vastness of the sea. The waves of the powerful seas pound against the rocks creating many favorable conditions to reef life such as ambient oxygen exchange, providing constant new sources of food, and the removal of wastes.
For the aquarist, an appropriate skimmer is essential as it will try to mimic this action creating fine bubbles for oxygen exchange while removing certain wastes. The addition and strategic location of pumps and filter outlets will serve the main function of the flow throughout the aquarium. There should be no place in the aquarium where the water is still or else anaerobic "dead spots" will occur. Don't worry too much about stressing the reef fishes and other animals as they are adapted to these conditions in the natural environment. The inhabitants will usually seek shelter among the live rocks if the flow is too strong.
Most of the reef life depend on good lighting as a source of food. That is right, food. All algae need light to create food in their system. Algae in the aquarium is important as it will serve as food for many types of fish and invertebrates. It will also use up the excess nutrients from leftover foods and wastes. A healthy aquarium is one that has some algae in it. Corals use algae in their bodies to produce food as well. This is the reason that corals generally need a bright light source.
A bright light source for the aquarium can be found in three popular forms: VHO (Very High Output) fluorescent bulbs, compact fluorescent bulbs, and metal halide bulbs. Some aquarists use a combination of these bulbs as well. Some concerns using these light sources are that they will generate heat and they usually are expensive. For more information on these bulbs, please use the links on my link page.
Aside from these three important aspects in starting a reef tank, there are many more things to do such as maintaining water quality by changing partial water every month or so, topping off with freshwater to compensate for evaporation, addition of essential minerals and elements (calcium, iodine, strontium, etc.), maintaining a correct and stable temperature (75 to 78 degrees F), regular feeding, cleaning of detritus, and cleaning of equipment. These topics are well covered on other web-sites (I might choose to add this to my web-site at a later time).
The best advice I could give to the starter reef aquarist is to research and plan ahead as much as possible before you begin this hobby and avoid an impulse buy. Also, reef aquariums do not necessarily have to be expensive. Finally, I have found that this hobby really disciplines me in other aspects of my life. Enjoy the little steps you take toward building a successful reef aquarium.