When and how to use fill-in flash, high speed sync and slow sync flash

Fill-in flash is useful in many situations, even if we only have the built-in flash at hand.
Even though an external flash offers a wide range of additional options and is recommended to achieve more professional results, the built-in flash is useful in many situations and can be slightly more versatile if we either make or buy an accessory called flash diffuser, which has the objective to soften  its generally harsh light.

What is fill-in flash?
Regardless of whether we are using the built-in flash or an external flash, fill-in flash aims to achieve proper lighting of our main subject, be that a person, a group of people or any other subject we want to emphasize over the environment, ideally in situations where there is a reasonable separation between the main subject and the background.
Although most people believe that flash is only used in low light situations, fill-in flash is useful in almost any daylight situation where we alternatively need to reduce the EV range of shot – like when the subject is back lit –, when we want to illuminate a subject that would be otherwise underexposed or poorly lit – when in the shade, for example – or when we wish to emphasize our main subject and at the same time reduce the brightness of the background which, typically, but not always, involves raising flash compensation (FEC).

Fill-in flash also allows to "freeze" a moving subject at slower shutter speeds (1/60 s. or less), for example when we pan with the subject, leaving the background with motion blur and the main subject (at least partially) sharp, depending on the chosen shutter speed and aperture.
It depends on the situation and the scene to photograph if we choose normal fill-in flash or slow sync in these situations, usually determined by the amount of available light and also dependent on whether the camera has high-speed sync (discussed later) available or not. 

Fill flash at slow shutter speeds and at night
While during the day we can usually make do with standard flash eventually combined with high-speed sync – if your camera has this mode – in low light situations we need a flash mode, which, depending on the brand and model of the camera, is called slow sync (SLOW) and rear-curtain (REAR), both available on Nikon cameras or 2^nd curtain in Canon cameras.
Slow sync ensures that the subject in the foreground is correctly exposed while preserving the brightness of the environment, which, with normal fill-in flash or front curtain, might otherwise be under-exposed or even completely dark.

The difference between the two is that while standard flash fires immediately after opening the shutter curtain, taking care of the illumination of the entire scene, slow-sync flash is only activated when the curtain is about to close, complementing the exposure without flash only to illuminate the subject in the foreground.
Slow sync gives an exposure that preserves the different brightness levels in a scene and is particularly suitable for situations in which we use longer exposures, like a sunset, a party, at night on the street or in any other location with low brightness levels in the foreground and with a visually appealing environment, when we typically use relatively slow shutter speeds.
That is: from 1/250 to 1 second or more, depending on the camera and the exposure mode selected. 

Slow sync flash comes in different flavors, not only depending on the camera model, but also on the chosen exposure program.
In some cases it may be wise to choose an Auto or Scene program over PSAM because they offer flash modes that can be more difficult to configure and control in the “creative” modes.
One example is the “Night Portrait” mode, available on most Nikon models, which uses slow sync with or without red-eye reduction by default, while the “Night Portrait”  mode of the Canon Rebel T3 and T3i apparently uses 2^nd curtain sync to obtain similar results.

Still, I recommend that once you understand the logic, you use the experience gained to set up the camera and internal or external flash in P or A modes, because they allow greater flexibility than the S or M modes and are far superior compared to the automatic scene modes that typically exclude more sophisticated levels of control, such as EV correction and flash exposure compensation (FEC), among others.
Independent of the slow sync mode used, the use of a tripod is recommended to prevent the typical camera- or motion blur resulting from shutter speeds at or below 1/60 of a second.
Also, in slow sync mode the flash fires 2 times; the first is a so-called pre-flash which is emitted before the shutter opens and is used to determine the correct exposure, while the second is the one that “counts”, just before the shutter curtain closes.
Therefore, it is important to tell the person or persons not to move after the first flash, because this will result – virtually without exception – in more or less motion blur in the subject.

Fill-in flash, limitations
Unfortunately for owners of entry-level cameras, be that Canon or Nikon, fill-in flash may come with certain limitations.
While the more sophisticated Nikon models have a high-speed sync mode called Auto FP, which is mainly used in high luminosity situations and allows the flash to sync with shutter speeds up to 1/8.000 s., in most basic models this function is absent.
High-speed sync is also available on the more expensive models from Canon, although with basic cameras high speed synchronization – unlike their Nikon cousins – can still be achieved with an external flash from the same brand, such as the 430 EX II Speedlite, for example.
On the other hand, most Canon models feature only one slow sync mode, called 2^nd curtain, which is limited to shutter speeds from 1/30 of a second and less (1/15, 1/8, 1/4, etc.).
At higher speeds, these cameras automatically convert to 1^st, or front curtain.
Nikon offers a wider range of options, including in its entry-level models: slow sync with or without red eye reduction and rear curtain with slow sync at shutter speeds between 1/250 and 30 seconds, depending on the exposure mode selected.

For more information on flash modes consult your manual
• Canon Rebel T3 (EOS 1100D): Night Portrait, p. 62 ff.; Flash Control, flash settings, p. 168 ff.
• Canon Rebel T3i (EOS 600D): Night Portrait, p. 63 ff.; Flash Control, flash settings, p. 180 ff.
• Nikon D3100: Night Portrait, p. 29 ff.; Flash mode p. 68 ff.
• Nikon D5100: Night Portrait, p. 23 ff.; Flash mode, p. 38 ff.
• Nikon D7000: Night Portrait, p. 42 ff.; Flash mode, p. 144 ff.
• Nikon D7100: Night Portrait, p. 42 ff.; Flash mode, p. 120 ff.
• Nikon D90: Night Portrait, p. 42 ff.; Flash mode, p. 71 ff.

For other models of both brands, look in the manual for the above mentioned terms; it may be convenient to download it in PDF format from the manufacturer's website to facilitate the search for any topic that you want to review.

You might also want to read:
Cool Stuff V. Godox Witstro AD-180 & AD-360 portable bare-tube flashes
Cool Stuff IV. The Strobies XS bracket: turn your hot-shoe flash into a studio flash