One thing I have always liked doing is getting close up fish faces and the eyes of the larger fish. You can have a lot of fun with this and if you are patient and approach the fish in a slow non-threatening way you will get good results. Clearly the fish that are camouflage wait and strike types are easier to approach. Others are just plain skittish and you will have little luck but most all can be approached to a certain degree. By learning a bit about the behavior of the local fish where you will be diving you too can get good results.
I am often asked what camera and other equipment I use when people see my photos. Although equipment is very important, one of my standard answers to that question is the best way to improve your photos is make sure your buoyancy is rock solid and you can remain nearly motionless in the water while holding your camera as well as being able to shift your position by using very small movements of your body and fins. Having a neutrally balanced camera rig will go a long way towards helping that buoyancy which is one of the reasons I am so pleased with my Beneath The Surface tray/frame set up. It was light weight from the beginning and the bar along the top allows for attaching trim foam to get it to that neutral buoyant state. I have mine now balanced to the point where I can shoot one handed underwater even with the heavy glass of either a 10X diopter or a large wide angle wet lens. Shooting one handed is a huge asset when trying to get in real close to a fish because the camera can be maneuvered without your entire body having to also be close.
Most fish I have found the best way to approach a fish is from slightly below and at an angle slightly to the right or left of the headon angle. I think the fish feel safe if they can “keep an eye” on you and that side angle allows them a quick escape vs. directly headon where they have to turn to run. This works for the smaller fish too, but many of the wall dwellers and hole dwellers like gobies and fringeheads, you basically have to just plant yourself and wait for them to come back out of the hole. Know that if you come up from behind or above they will almost always bolt.
I am shooting with continuous lighting. If you shoot video you would also be using this same approach. What I do is turn on the light before I aim the camera at the fish so that the act of turning on the light itself does not scare the fish away. I then slowly raise the camera up and aim at my subject. Next step is to start moving in very slowly with as little movement as possible and while not holding my breath, I try to exhale as few bubbles as possible until I get off a few shots. After I get my shots I then back away just as slowly trying not to disturb my subject any more than I have already by shining bright lights in its face.
Meet some of the Southern California locals, face to face, and eye to eye!