Ocean photography isn't all that much different from land photography except you are dealing with buoyancy instead of gravity, sharks instead of dogs, and trying not to drown.
Did that sound intimidating?
The middle bit was a joke, but buoyancy and not drowning are certainly realities. Tip number one of amateur ocean photography is simple to say, but not so simple to accomplish. Once you have accomplished number one, the rest will be easy.
If you wish to learn the 6 Tips in video form, you can see it here:
Tip 1: Learn how to freedive
Yes, that "sport" that involves holding your breath and diving deeper - going against all of our natural instincts. Let's face it, a shot of a turtle from three feet away is a lot more interesting than a photo from 20 feet away. You are not going to magically make it to 20 feet without some practice and training. And if you do, you'll be on your way back up as soon as you hit it, wishing you hadn't gone so far. Learning how to freedive will also make your movements steadier... I'll address that again later. As you can see from the photos below, freediving makes for much better photos than floating at the surface.
Tip 2: Gear - Fish-eye or Wide-Angle and Zoom or No Zoom Function
If you do not know how to freedive, I would not recommend buying or using a camera that has Fish-eye and no zoom, unless your subjects are 22-foot tiger sharks or whales.
Here's the thing - if you cannot freedive, you will not be able to get close to your subject unless it comes to the surface. Fish-eye lenses make the subject appear smaller and further away than they actually are. The only time that I was happy to have a fish-eye was when I encountered a manatee of about eight to nine feet in length while snorkeling in Vieques. Even then, the fish-eye was only appropriate because I dove down and swam right next to the manatee.
Hopefully by now, the zoom versus no zoom is clear - same reason. If you cannot get close to your subject, you might want the ability to zoom.
Tip 3: Red Filter
In the ocean, the first color that you lose is red within the first 15 feet. In order to have full color in your photos, you will want to use a red filter depending on the depth and the camera. My Sony Mark V lets in a lot of light, so I do not use a red filter within the first 15 feet, but I do have to color correct the photos. With my gopro, I almost always use the red filter unless I am shooting towards the surface. Many cameras come with a selling point of an automatic "White balance." I have found that it is never quite sufficient. Keep in mind that some cheaper waterproof cameras may not have the option to add an external red filter.
Tip 4: Energy
What? Do I have to get hyped up on caffeine?
No. Quite the opposite.
Just like with human to human interactions, your energy around sea life matters. The turtles, for example, will pick up on your energy. If you are too frantic or your movements are too jerky, they will not want to be around you. If your goal is a quick shot and you swim as fast as you can towards that surfacing turtle, he or she is going to split before you get that click. If your energy is calm and respectful, you will find that sea life will move towards you instead of away. I have had many encounters with turtles in Vieques that have swam towards me at the surface to arrive to a point so close that I cannot capture their entire body in the frame (inches away from my face).
Tip 5: Surroundings
Be aware of what is behind you and what is in your frame. There are a lot of factors to deal with in the ocean. When compared to land, you could say that the ocean is more like a 3D space, while land is a 2D space. If you are under a pier or next to a breakwater, shoreline, or shallow area, you do not want to damage the local environment or hurt yourself by bumping into things because you are focusing on your subject.
Just the same as paying attention to what is behind you, you need to be aware of all the subjects in your frame. The reef is a busy place; your photos will end up messy and unfocused if you do not isolate a subject.
Here are two very similar photos, neither are award winners, but the one with the 3 fish around the turtle's head is too busy: