It takes patience, creativity, good composition/understanding of photography (same skills as topside, with adjustments for loss of light at depth, etc.), adventure and the pure love & curiosity of the under-water world..... but the hands down number one requirement is EXCELLENT scuba-diving skills, most importantly buoyancy and air consumption. PLEASE do not get into under-water photography until you have a good base knowledge and substantial experience in scuba-diving itself. I have witnessed too many beginners, whom attempt photography before mastering their skill of diving, hurt themselves and others, and honestly their photography suffers as well. Get your scuba certifications, including advanced, log your dives and hours, take the underwater photography cert course and sign-up for dive trips centered around honing your photography skills and DIVE SHOOT DIVE SHOOT DIVE SHOOT REPEAT!
Now with regards to equipment, you don't have to break the bank spending thousands on a camera, housing, strobe, etc. -- you can start with a lower priced entry model with good quality that sets you up with the necessary basics to shoot phenomenal images under-water. Sealife is a great company, as is the ever popular GoPro; however, if you already have a topside camera you love (Nikon, Sony, Cannon, etc) you can investigate adding on the housing, lens and strobes for your specific camera model. Either way, there are many options at great entry prices which produce stunning images -- have fun exploring!
Personally, I have an INCREDIBLE passion for scuba diving and under-water photography, but I am not a professional -- this is my hobby, so take my advice with a grain of salt. Ask others, consult professional resources, attend Scuba Diving consumer shows, etc. - do your homework and research before jumping in. It's amazing and an addiction, the desire to capture these unbelievable and magical moments & marine-life to share topside with friends & family -- only 1% of the world's population actually gets to explore 70% of the world's surface (our oceans) -- it truly is a rare, otherworldly and beautiful experience! So if this is your passion, go out and learn, dive and make stunning photography to share with the rest of the world... just make sure to be a responsible diver and respect the ocean! Take pictures, make memories, but love & help the ocean by educating others... it's the soul of Mother Earth and vital to our planet's health!