The question comes up then, how does the camera know for how long to keep the strobe on in order to produce a good exposure? This is solved by using what is called TTL (through-the-lens) metering. When you press the shutter button, the camera takes two photos in quick succession. First, it takes your aperture, shutter and ISO settings, opens the aperture and fires a very brief flash pulse (this is typically called pre-flash). The resulting photo is almost always underexposed, but it's not even shown to you or saved anywhere - instead, it is used by the camera's processor to gauge by how much it was overexposed, and once that calculation is complete, it can decide how much flash power it needs to add to produce a proper exposure. Once that is done, the camera takes a second photo, this time for real, using the calculated required flash power, and this is the photo that gets saved to your memory card.
When you're using off-camera TTL strobes, such as SeaFrogs ST-100, they act as a simple amplifier to the camera's flash. When the pop-up flash emits its pre-flash pulse, they also flash briefly, and when the camera emits the main flash, they stay lit for as long as the camera's flash stays lit. The camera is only aware of the increased amounts of light coming in. One point of note, however, is that if the light transmission through fiber optics between the triggering pop-up flash and the off-camera strobes is poor (as it can be with poor-quality fiber optic cables) and/or the off-camera strobe's sensor is not particularly good, the off-camera strobe can miss the brief pre-flash, causing the camera to take effectively a wrong reading and fire the main flash pulse at too high a power setting. This has a very high chance of producing overexposures.
Now, translating all this theory into practice, we come back to our settings. ISO 100 gets us maximum dynamic range, so that's a given. This gives us the first point on the exposure triangle. For aperture, f/5.6 is a decent middle-of-the-road setting, so let's start there - this gives us our second point. Now, we need to take into account foreground and background separation - while shooting with strobes, the strobe light dissipates quite quickly with distance, so only objects very close to the camera (foreground) will be lit by strobes, while objects further away from the camera (background) will be lit by ambient light only. Therefore, for the background, our exposure triangle will be formed by ISO, aperture and shutter speed. Suppose a shutter speed of 1/250s produces a level of exposure that is acceptable under your specific circumstances, which can change with time of day (angle of sun in the sky), cloud cover, water clarity, depth, etc - but let's assume 1/250s is good enough for our example.
The last and possibly most important part is the strobe output and its effect. When the subject of your intended photograph is close to the camera and strobe, the light emitted by the strobe, reflected by the subject, and carried through the lens onto the sensor will be significantly brighter than the light emitted by the sun and reflected by the subject into your camera. This is important while shooting underwater because sunlight is filtered through a large amount of water, which absorbs longer wavelengths (red and yellow) far more than shorter wavelengths (green and blue), so at depth, you get the characteristic blue/green tint. When the white light emitted by strobes, which did not travel through tens of meters of water, dominates the exposure, then you get the bright, vivid colors that you can't really get otherwise. However, and this is largely specific to underwater photography - in most cases, not all of your frame reflects strobe light. In many cases, much of your frame will consist of clear water, through which your strobe light will go out and dissipate, never to return. This is where it gets very important that you understand how the metering modes work in the camera. The default mode is Multi - it divides the frame into areas, measures the brightness of each area individually, and tries to come up with a balanced exposure. Underwater, with lots of water in the frame, this is bad, bad, bad - the camera will evaluate the water as badly underexposed, dial up the flash output, and badly overexpose the subject in its vain attempt to light up an entire ocean. The second available mode is Center - this measures the average brightness of the entire screen, while emphasizing the center - it is less bad, but still mostly unacceptable underwater for the same reasons as Multi. Finally, there is Spot - this is the setting that I use underwater with my A6300, as it only evaluates the center of the screen, and ignores everything around it. This way, so long as you compose the photo with the strobe-lit subject in the center, the camera uses the strobes to light up the subject in a way that is not too dark and not too bright. If the background is too dark, you can open the aperture to admit more light into the lens, and the camera will automatically dial down the flash power to compensate, or you can reduce shutter speed at the same aperture and this will have no appreciable effect on flash power and thus foreground exposure.
TL;DR: For clear tropical water at moderate depths in good weather, ISO 100, f/5.6, 1/250s, spot metering, TTL flash, subject in the center of the frame should produce something approximating decent results. Get as close as you can to your subject and play with aperture and shutter speeds to adjust background exposure levels. Shoot in RAW format and many mistakes can be fixed in post-processing.