I don't understand why many a times Bob answers with so many reservations on the words and the answers are not so helpful...
Anyways, I am another A710IS user and I had this problem in the beginning as this is my first Canon. My previous one was Fujifilm.
The noise in the picture doesn't really depend on what picture setting you choose like superfine or fine, that is the compression level for jpeg file format. Of course, superfine will be much better than fine but that is not what you should be looking at.
The other reply has offered you enough advice to start looking at but what I do is, using manual mode. Keep ISO 80, highest I will go is ISO 200, if its too dark around (but then I will see enough noise in the picture) Keep longer exposure times and bigger aperture. You will have to do this using a tripod or with stable support like a bench or so. If the scene is not well lit and if you use flash then depending on the scene, you have two options. If you are shooting indoors then you may get your problem solved and you will have a nice picture but if this is say, evening shot of the landscape then, it will be more darker than what it is to your eyes so there you will have to switch off the flash and expose it for longer duration. The major catch here is your ISO speed, if you leave it on Auto then it tends to choose ISO 200 or 400 depending on the illumination and the worse part is this ISO is not quickly visible in EXIF. There is some tweak to figure it out. You won't see it under informative display mode either (press display button till you see a histogram below the picture)Choosing this higher ISO ends up with a noisy image.
So indoors I use flash to default level and most of the time, my problem is solved but if this is landscape picture then I will not use flash. As said before, the picture will be dark. I use a photo editor and manipulate with shadows and mid-tones. thats it. The problem solved.
I must say that A710IS has a bit of learning curve, depending on what your experty is and which cameras you have used before. I am yet to explore all scene modes.
Still you fail to solve the issue, then I recommend you to spend some 30-40 USDs on noise manipulation program like Noise Ninja or Neat Image. I read the reviews saying they do a quite decent job.
OTHERWISE, replace your A710IS with Fuji FinePix F30 Zoom, if its still possible.
Hope, I have made the point in this rant, else post back and may be we could take it with some example.