Obviously there are different strategies for different situations, I usually use an iterative process that goes a little like this:

• Do I want a particular aperture for artistic reasons (e.g. blurred background)? Do I need a specific aperture for technical reasons (getting multiple subjects in focus)?

If yes, set it, if not pick something optimal like f/5.6. Then I look at the shutter speed and ask similar questions:

• Do I want a particular shutter speed for artistic reasons (e.g. motion blur/light trails)? Do I need a particular shutter for technical reasons (e.g. to prevent camera shake)?

If yes, set it, if not pick something "safe" e.g. 1/2*focal length. Then I look at the exposure and set ISO - there's no artistic consideration here (if I want noise I'll do it in Photoshop so I can get a nice fine grain) so the only question is:

• Do I need to reduce noise (e.g. if I plan to do a lot of editing)?

If not, set the ISO to whatever is necessary to get the correct exposure, even if it seems quite high! It's important not to underexpose as this is much worse for noise than upping the ISO. If there isn't a high enough ISO, or I want to reduce noise by letting in more light, I will go back to the earlier questions and re-evaluate any arbitrary decisions. If I can open the aperture I will, likewise if I can slow the shutter I will.

If not it's time to make a compromise and weigh up how important the artistic and technical decisions were, until a sensible balance is achieved.

This sounds quite complicated by I usually run through this in my head a few times by guessing what the exposure will be before actually setting the camera. It's also fine to use auto mode to fill in the aperture/shutter as appropriate if you're not setting it for creative reasons (the OP seemed to be asking about full manual settings).

Throw in flash an you've got another variable, with another art/technical trade off. It gets a bit complicated to generalize here, in general I'm either using flash for artistic effect in portraiture in which case flash rules and all other settings bow to it, or I'm using it for extra light in event/wedding photography, where I set the aperture and shutter how I want them both artistically and technically and use the flash to pick up the slack, going back to the other settings if I need faster recycles or want more ambient in the background.