Trying to get into 'stuff' instead of gear...

Why use a flash?

a) Add light when dark.
b) Fill flash (opens the shadows in a brightly lit scene - think of light source placed behind the main subject)
c) Separation the flash light overwhelms the ambient light. Using this method one can create appearance of night in broad daylight I use that routinely in macro and close ups.
d) Other uses (modeling, transparency...)

Four generic camera dependent flashes:
- Pop-up Close to the lens axis prone to create red eyes. Shark shadows.
- On camera (shoe) also can create red eyes and sharp shadows. One advantage (and potential issue) is that one can bounce the flash and orient the flash head 360 Horizontally and 180 vertically. The orientation will determine where the shadows will be. Note that the shadow can be somewhat controlled.
- Specialty flashes such as ring flashes for macro and sometime portraiture
- Flash gun mounted on the side of the camera (Sunpak, Metz by example). These camera offer an independent power source which means that they are more powerful and can generate more flashes than the measly batteries used by shoe flashes. These can operate as slave to the camera for exposure or triggered by the came using a sync cord or wireless.

Off camera flashes
Number (of flashes), settings and positions depend of the desired final result. Usually used in studio for refined control. Outdoor flashes are similar to these, just not as accurate (opinion).

Note that light created by a flash or flashes drops off quickly. The more powerful the greater the drop off distance. Accessories can augment the range (concentrates light in a narrower beam). Flashes, especially in camera have a tendency to flatten the subject.

Basics of using a flash.
All camera have a default sync speed, usually 1/60. If you look at your camera manual you will find that the real sync is often higher. Nikons by example sync at 1/250.

Rear/front curtain
This can be confusing but it really needs not to be.
Consider that the front curtain camera setting triggers the flash the moment the sensor is fully open. This creates the initial exposure then the action keeps on going until the curtain closes. (motion blur is inside the object) object + motion [Left to right]
The rear curtain on the other hand means that the flash trigger the moment the curtain is about to close. The sensor has already recorded all motions during the exposure and the flash freeze the last one. (motion blur is outside the object) motion [Left to right] + object

Flash duration. I varies from flash to flash and this should be part of your flash selection when purchasing one.

Flash alternatives exist from additional continuous lighting (heavy, cumbersome, limited range - think video light) to reflectors (light weight - may need an assistant of more to orient them correctly).

How to select a flash?
After selecting between shoe or gun flash
Two things to look at:
1) Power as in guide number (GN). The greater is the best (more light). GN depends on: Aperture, Distance and ISO Default value: f1, 10 feet, 100 (default value). More often than not flash are 'zoom-able' in this case the GN reflects the longest possible zoom setting. on a 24~105 the GN will be for the 105. The 24 GN is much lower (light diffusion) so beware.
2) Flash duration

This is a broad approach to flashes, nothing else. It is not meant to teach how to use a flash but to inform on its potential use and effects.