Okay, get a cup of coffee because this is one of my favorite subjects. I've had to teach so many assistants and second shooters this stuff I can do it in my sleep. Hopefully, I won't put you to sleep ... :ROTFL:
Like you, I'm slow to read manuals, and even slower to read all the stuff on web sites because, for the most part, I don't like or can't relate to the photos used as examples there ...
I use flash to some degree on almost every shot I take with a DSLR (not ALL, just a majority), leaving the available light work for the Leica M and fast M lenses. How much you may use it or not is your decision.
However, I personally feel that flash is a maligned tool, especially on-camera flash ... partly because it's usually overcooked or misdirected.
So, the objective is use it, and make it hard to detect that it was used. The following applies to any use of flash on any camera, the A900 is no different.
Unfortunately, there are no wholesale solutions that lead to pat settings, just basic principles of achieving
"light balance". Light balance between the background and the foreground subject is the initial goal, from there you can creatively decide how you may want to alter that balance for effect.
In darker ambient conditions where flash is often essential, there is a simple notion to remember: The camera settings control the background exposure, and the flash settings control the foreground exposure.
One of the chief techniques in darker conditions is called
"Dragging The Shutter." This is the use of a slower shutter speed to open up the background ambient lighting rather than having a wall of black behind the subject.
Rule of thumb in "cave" like conditions along with suggested settings:
1) set the camera to Manual. Choose the highest ISO you feel the camera does well with (IMHO, on the A900 it's ISO 800, maybe 1000) Set the shutter speed as low as you feel you can handhold for exposing the background ... (in-camera IS of the A900 helps here). Set the lens aperture to the widest f stop you can and still achieve the DOF needed for the foreground subject. The objective is to get as much ambient background recorded as possible.
I usually do not meter the background at weddings ... there isn't enough time to fiddle with settings, and it's usually pretty dark anyway ... so I expose it to the best of any given camera's ability.
2) Set the flash to TTL. The flash will expose the foreground subject AND help freeze the subject motion because of the "duration" that the flash is actually "on" is far faster than the camera shutter speed. At an extreme, this is how splashing water droplets are photographed ... nano second flash duration.
Flash Compensation: to increase or decrease the exposure on the foreground subject, you ride the flash compensation, which increases or decreases the duration that the flash is "on". (On the A900, you can assign flash comp control to a button that brings it up on the LCD making it easy to see even in a cave ... a very fast and easy function to perform compared to the SB800.)
The benefit of using the camera and flash in this manner is that it puts far less strain on the flash, and recycle is quick most of the time. Basically, its fill flash 85% of the time rather than being the prime source.
Second Shutter: by setting the camera to "Second Shutter", the flash fires just before the camera shutter closes instead of just after it opens. When you drag the shutter using even longer shutter speeds, subject motion may occur ... second shutter makes sure that the motion blur trails the subject rather than overlapping it. (see sample of Greek Dancing below).
Off camera: You can take the flash off the camera and aim it anywhere you want. The A900 has this capability. I hold the camera in one hand and the flash in the other ... which is why a hand strap is essential for the way I work. And the Sony hand-strap is one of the best I've ever used. (see the example of the Sax player lit by holding the flash down low.
Here are some examples shot in very dark conditions OR back lit conditions where light balance technique was employed: