Are you shooting dark rooms / night time shots? I presume so with a 10s exposure! lol
Be aware that 10 seconds is 10" on the LCD display, not 10, as 10 is 10th of a second
I find that on the S6500fd you can still see a preview of what you're shooting on the LCD regardless of what settings you have, but if you have it on Manual and have incorrect settings, the picture will just come out too dark or too light.
You are right to assume that you change the F numbers by pressing the button by the shutter button and then pressing up and down on the navigation thingy on the back
Your best bet is to not worry too much about F numbers at the minute and concentrate on working out what sort of effects you get with different exposure times.
Get it set up in a fixed position, then go from a quick exposure to a long exposure - then you can see what it's like when it underexposes and overexposes.
Then, when you've got a feel for how long you need to expose a pic for, set the ideal time and play with F numbers from one end of the scale to the other. They make quite a difference to the brightness of the picture.
Ideally you'll get to the point when you know what F numbers to use in conjunction with what exposure times to get a good picture - but that's partly why I use Program mode quite a lot, as that's what it does for you (gives you the range of shots you can get away with).