First of all, I never change ISO unless I need to. If you're changing ISO a lot (and not using auto-ISO) then I can get that it would be very complicated.
I like to use ISO as close as possible to my cameras native ISO, which is 200 on both my Sony and (I think, anyway) Fuji. If I need less exposure, I consider ISO like a "boost in sensitivity" - which it is. It's not really an exposure control, because it does not affect the amount photons on the sensor, it's more of a camera setting. (back to ISO in a bit)
Now that I have ISO tucked away in the corner, it's a little easier to think about shutter and aperture. Here it's a simple give/take relationship. If you stop down one whole unit (f-stop) then you must increase exposure time by a factor of two in order to get the same result. This is because each f-stop is calibrated to cut light by half. If your background is as sharp as you want it, but your meter is reading two "equivalent values" (EV being equivalent to one stop, twice as "bright") under what it should be, then you need to decrease your shutter time by a factor of four. (i.e. from 1/250 to 1/60). If your hands are too shaky to shoot at 1/60, then you'll need to open up the lens by one stop (say from f/5.6 to f/4) and decrease your shutter speed to 1/120.
So it's all about give and take. Now, back to ISO.
Sometimes you have no choice but to adjust ISO and introduce some degree of noise. I worry about this less with my fuji being that it is a pretty good performer in low light. On my a700 DSLR on the other hand, I need to be more careful. What is an acceptable level of noise is up to you.
ISO will literally turn up the signal off the sensor before it is converted into digital data. It is a very similar process as turning up the volume on your stereo. So when you do that, everything will become more exposed when increased, and less exposed when decreased.
So let's say that on that shot you couldn't hold at 1/60 the background looked perfect at f/4. Your only option would be to increase ISO. Don't worry too much about what ISO numbers mean, it predates digital and using it this way is kind of silly anyway.
What you need to worry about is that every time you double the ISO, you're sensitivity doubles as well. This will allow you to cut the exposure time in half while keeping the aperture the same (or stopping down once and keeping the shutter time the same if need be).
But again, I tend to think of ISO as a last resort option. Many modern cameras are a lot more flexible in this way, though, so maybe you might find it useful to adjust it more frequently. But for me ISO is just something I don't think a whole lot about until the sun starts to set.
Still, it might be beneficial if you first learn aperture and shutter speed and get a good feel for exposure equivalences before trying to balance a three-way teetertotter.