There are several technical factors that will affect your images directly which you have control over. Depending on each situation that you want to shoot, you may want to have the others adjusted automatically by your camera, or adjust all of them manually yourself. Shooting moving subjects generally means shooting in Shutter priority mode and shooting portraits usually means shooting in aperture priority mode or manual mode. Doing serious flash photography, you will almost always use manual mode to be able to expose freely.
This is a property of your lens. Focal lengths are normally given as 35mm equivalent focal lengths, that is to say, the length given on the lens indicates the focal length when used with 35mm film, or a full frame sensor. Focal length along with aperture, affects depth of field, longer focal lengths generally having a larger effect on the amount of blurring than just a wide aperture.
This determines just how wide your lens will be opened once the shutter is triggered. It directly restricts the total amount of light that is going to hit your film or sensor, and as a result, controls all lights in your image, whether they are there for the entire duration of the exposure, or only appear for part of your exposure, like a flash, or a car entering your image at night in the middle of your exposure.
Depth of Field
The depth of field of an image is the distance in front of and behind the subject you focus on which is in focus. Wide apertures give you a shallow depth of field, allowing you to blur your backgrounds to draw attention to your subject while closing down your aperture allows you to get a wider shot while keeping several subjects at different distance in focus.
The light of a flash is instantaneous, as such, if you are using flash with constant power (Manual flash settings), you can adjust the effect that the flash is having on your exposure precisely by changing your aperture.
Exposure length is the length of time that the shutter will remain open once triggered. This controls just how long your sensor will be exposed to light. Exposure length controls whether you can shoot a photo hand-held without camera-shake affecting sharpness as well as how subjects appear in the image.
Short exposures allow for shooting still images of subjects in motion, things that the naked eye cannot perceive as anything but a blur. For really high-speed photography, additional light sources are a necessity.
Long exposures can be used to get a bright enough exposure under low light conditions, or, combined with a circular polarizer filter / ND filter used to capture motion in a still image. Moving lights will appear as streaks in an otherwise unmoving frame.
Long exposures with flash
Flash used at the beginning of a long exposure will cause the subject to appear to be frozen at the beginning of their motion while the rest of their motion appears trail off of this first image. The backlights of a moving car would actually become a streak of light over the car in a photo shot this way.
Flash used at the end of exposure is generally called rear curtain flash and allows for motion trails to lead to the sharp, well exposed image in a long exposure. The backlights of a moving car shot with rear curtain flash would become a streak of light behind the car.
Combined with the focal length, shutter speed also determines if an exposure can be made hand-held, a rule of the thumb on this is to match focal length to shutter speed - so if you're using a 50mm lens, shooting at 1/50 or faster, or 1/200 with a 200mm lens is supposed to give you about 100% blur free images if you have relatively steady hands. However, image stabilization on a lens affects this, and it is possible to shoot at high-speed burst modes and get completely sharp photos with an unstabilized lens at speeds approaching even 1/4 of the speed the above rule would suggest as the rule only really applies to probabilities - the human nervous system has completely normal, random muscle shakes several times a second, so if there's a 25% chance that a given shutter speed is long enough to include a shake, there is still a possibility that this won't happen and the image will come out sharp at that speed if you simply shoot 4 times - this is why it's a good idea to use high-speed burst mode at low light conditions.
The ISO value is a property of the film or the sensor in your camera. Basically, it is the speed at which the film or sensor absorbs light. The faster this speed, that is to say, the larger the ISO, the grainier an image will become, especially in the darker parts. However, the slower (smaller) ISO numbers will not only result in a much cleaner image, but will also require more light to properly expose. Unless you wish to achieve a certain grainy look, try to shoot at the lowest ISO level that your other considerations for your image will allow you.