There are four basic settings on most cameras that affect the picture; the focal length of the lens, the shutter speed, the lens aperture (size of opening), and the film or sensor sensitivity called ISO.
Focal length affects the size of the area that is captured (close-up or telephoto).
The others affect the exposure, how much light from a scene is recorded.
Low end cameras allow you so set the zoom level but determine the exposure automatically.

How Aperture and Shutter Speed Determine Exposure:
Most middle and high-end cameras have a semi-manual mode which allows you to fix some exposure settings while the camera automataically adjusts others. The primary uses are:
Aperture Prioirity - You set the aperature (lens opening size) - Primarily used to change the depth of field (distance range in focus).
See depth-of-field range below.
and
Shutter priority - Used to blur or freeze motion, especially for sports or to avoid bluring from camera shake during handheld shots.
A very slow shutter speed will blur a mountain stream, capture star trails moving across the sky, and blur moving objects to give a powerful sense of motion.
See Shutter speed below:

Higher ASA's will allow you to have faster shutter speeds, but you will loose some picture quality.

F number:
The F stop number is the focal length divided by the aperture diameter. The larger the number the smaller the opening.
Is a measure of light gathering capability which depends on how wide the opening in the lens is.
Typically the minimum starts from f/1.2 - f/4.5.
Since the light gathering is proportional to the surface area which is π*r². they go up in steps by a factor of √2 e.g. 1.4, 2, 2.8, 4, 5.6, 8,11,16,.., each step represents twice the light gathering of the previous. Typical values include half and third stops:

F value	1.2	1.4	1.8	2.0	2.2	2.5	2.8	3.2	3.5	4.0	4.5	5.0	5.6	6.3	7.1
stops	0.5	1	1.7	2	2.3	2.7	3	3.3	3.6	4	4.3	4.6	5	5.3	5.6
F value	8	9	10	11	13	14	16	18	20	22	25	29	32	45	64
stops	6	6.3	6.6	7	7.4	7.6	8	8.3	8.6	9	9.3	9.6	10	11	12

Examples of combinations which will produce the same exposure as shutter speed is doubled (cutting the time in half - allowing half as much light) and aperture is increased by one f/stop (letting twice as much light).

Bright summer day ISO=100 or Low light outdoors ISO=400
Shutter Speed	1/4 second	1/8	1/15	1/30	1/60	1/125	1/250	1/500	1/1000	1/2000	1/4000
f/stop	f/45	f/32	f/22	f/16	f/11	f/8	f/5.6	f/4	f/2.8	f/2	f/1.4

Low light outdoors ISO=100
Shutter Speed	1/4 second	1/8	1/15	1/30	1/60	1/125	1/250	1/500	1/1000
f/stop	f/22	f/16	f/11	f/8	f/5.6	f/4	f/2.8	f/2	f/1.4

Bright room indoors ISO=400
Shutter Speed	1/4 second	1/8	1/15	1/30	1/60	1/125
f/stop	f/8	f/5.6	f/4	f/2.8	f/2	f/1.4

See: A Tedious Explanation of the f/stop from Matthew Cole.

Aperture and Depth-of-field:
Most advanced cameras allow you to select Shutter or aperture priority. Shutter priority means that you pick the shutter speed and let the camera figure out what aperture it should use. Aperture priority is the converse - you pick the aperture and let the camera pick the shutter speed.

A larger aperture (smaller f/stop number) reduces the depth of field, so your background will be fuzzy.

50 mm lens
F/value	1.8	2.8	4	8	16	22	32	45
In-focus range	1'	1.8'	2.5'	5'	13'	24'	400'	inf
Near	9.5'	9.2'	8.9'	8'	6.7'	6'	5'	4
Far	10.5'	11'	11.4'	13'	19.5'	30'	405'	inf
105 mm lens @ 10'
F/value	1.8	2.8	4	8	16	22	32	45
In-focus range		0.4'	0.6'	1.1'	2.2'	3.1'	4.7'	6.9'
105 mm lens @ 100'
In-focus range		40'	60'	160'	inf	inf	inf	inf
28 mm lens @ 10'
In-focus range	3.6	5.9'	39'	inf	inf	inf	inf	inf

See: Online Depth of Field Calculator
Max Lyons Depth of Field Calculator Determinants of DOF at Digital Photography For What It's Worth (dpFWIW.com)
The Ultimate Depth-of-Field Skinny byt Jeff Donald

Shutter Speed:
Telephoto lenses are more subject to blurring with if the camera shakes, because a small movement in the lens is magnified. The general rule for handheld pictures the minimum shutter speed is the reciprocal of the lens focal length for "acceptable" sharpness. e.g. 1/50 sec for a 50 mm lens, 1/200 sec for a 200 mm lens. A rangefinder can use slower speeds by one to two stops than a SLR.
Lens stabilization allows you to go down 3-5 stops. Optical stabilization (in camera) allows 2 stops. Sports Photography:
For small kids 1/125s or 1/250s may be fine. For larger, faster kids, and faster athletes in general, 1/250 is often the absolute minimum, and 1/500 is great if you can get it. If you can get 1/1000 you'll freeze them like stone.
Some people prefer aperture priority and others shutter for sports.

If you are taking pictures of something like a tennis match and your distance is constant you may want to set it to manual focus to avoid it changing to pick up the hat of the person in front of you.

See: Sports Photography at Nikonians.org
Achieving correct exposure with aperture and shutter speed at DigicamGuides.com

See Image File Formats

Glossary:
See Photography

Books:
Manual of close-up photography by Lefkowitz

Apps:
Android apps - iPhone/iPad apps

Links:
Cameras
Photographing Documents
Notes
Night Photography
Photography Cameras Lenses Filters
Photographing Documents and Historical Object Photography at my genealogy site.
Photographic Tutorials at Caz Mockett's blog
Photography articles, Living Bird | birds.cornell.edu
Photography: Share, Learn, Create in the Photography.com Community
Tutorials at Andre Gunther Photography
Article Index at Digital Photography For What It's Worth (dpFWIW.com)
Photography: Taking Pictures/ at sympatico.msn.ca
Tips & Tricks at RonBennettPhoto.com
digital-photography-school.com
www.creativepro.com
photodoto.com
A Focus on Storytelling - Travel Photography - WSJ interview with Bob Krist