Lars - Maureen said in her OP that she can’t duck dive (i.e. snorkel down) yet.
Maureen - unfortunately, if you are shooting from the surface, your results are going to be very limited, if only from the point of view of composition (i.e. all your shots will be looking down at the reef / fish, which is one of the least satisfying compositions underwater, and which most texts on the subject advise you avoid). So, if you can learn to duck dive, you are going to be in a much better place from which to shoot, enabling you to get low, and shoot up.
Have you considered learning to scuba dive? That would enable you to get down amongst the fish, and take your time sorting out your camera settings and experiment with different combinations to see what works and what doesn’t. Snorkelling involves alot less gear, and doesn’t require a certificate, and there are some u/w photographers who exclusively shoot whilst breath-hold diving (i.e. snorkelling), however they are generally very accomplished snorkellers able to duck dive for a good length of time (probably in excess of 1 minute).
Personally, I’m a pretty poor snorkeller - I can duck dive to 4m or so for a few seconds, but I’ve never managed to shoot any worthwhile pictures whilst doing so.
Anyway, camera settings. I’m afraid I’m going to disagree with Lars on a couple of points. In shallow depths, the automatic settings with underwater scene mode on your camera should do a perfectly good job. Blurry images may be the result of camera movement, or the camera not getting a good focus lock. Make sure you are letting the camera focus lock by half pressing the shutter button until the focus lock is achieved. Then if the focus is on the subject you are interested in, finish the press of the shutter button to take the picture. Try to keep the camera as still as possible, just as you do on land. If you are bouncing about in waves on the surface, this is not an ideal situation!
Your example shot is a fairly wide angle shot, and demonstrates a difficulty of wide shots. The background / far distance looks cloudy and fuzzy, due to the limits of visibility underwater. If you are able to get down, and shoot upwards, instead of having the far distance in your shot, you will get the water surface, which is closer, and a distinct object, so the shot will appear much less cloudy and fuzzy.
Hope that helps