As someone who spent most of the time shooting less than average landscapes, flash, and I mean pop-up flash as well as off-camera flash, has been in my eyes unneeded.
However after the "revelation" from master of portrait photography and famous painters like Velasquez and Rembrandt, I have understood what good lighting can do for your photography. From setting up the mood to sculpting out your subjects face features and adding textures. Off-camera flash is your best friend in pretty much any scenario.
On my recent trip to Varanasi I have done exactly the same. I "painted" with light on faces of people I have photographed.
Let's assume that you have already decided to use a flash on your shoot. First of all you need to decide what kind of flash you would like to use. On camera flash is a real savior if you need to quickly fill in shadows in broad daylight. Mind that the flash mounted on the top of your point and shoot or DSLR is going to give you a harsh light - this is due to its size. And also the light is coming directly to your subject thus creating a very flat portrait. Flat meaning there are no shadows and shape of the face is not pronounced and may seem very two dimensional - not a flattering or exciting light. Harshness or softness of light on your subject depends on size of a light source and its proximity to the subject. Big and close will give you soft wrapping light and border between light and shadow will be very soft. Small light source that is far from the subject will give harsh light with harsh shadows and hot spots.
Once you improve, and invest bit more in your gear, you might start using some sort of flash gun either mounted slightly higher on the top of your camera or off to the side. Now different angles come to play and your subject will have some areas of shadow and light on them. This will create more natural look and helps to show real structure of face features.
Let's have a look at off-camera flash bit more. Flash guns are pretty easy to use these days. Camera measures scene and tells your flash how much power to use. You get correctly lit photo. For more creativity you can tell your flash to either underexpose or over expose the scene. This however has its limitations. If you only want to light certain part of your scene your better use the manual mode and experiment a little.
This is the way I light my photos (not necessarily right, best or easiest way). First I take a reading for a whole scene without using a flash. I make an exposure then look at the picture and at the histogram and decide how much under or over I want to go. Underexposing ambient light suits me more as it adds drama to my style of photography. I aim for a darker more dramatic sky and background. When I'm happy with exposure I will introduce flash to correctly expose my subject. You can use a light meter to get this exposure right straight away or again - experiment. Zoom in as much as you can on your camera and look for shadows and light parts of the picture, hotspots, over or under exposed parts.
Paying attention to ambient light is in my opinion as important as your main light. Placing your subject in parallel line with your flash and ambient light i.e. the sun will give you very nice highlight on hair and shoulders, backlighting your subject in warm glowing light. This is easily achieved early in the morning and during the sunset.
Now it’s time to concentrate on quality and direction of your light.
Quality meaning harshness or softness and how the light is interacting with subject. For my portraits I prefer soft wrapping light with nice transition between light and shadow parts of the image. Flash hitting the subject directly will give you contrast look while flash pointed slightly to the side, where subject is only hit by part of the light emitted will produce softer light. Soft light is very flattering for female subject and more contrast light for male models. This of course depends on your taste, subject you are portraying and feel you want to get out of your photograph.
Direction of light and how it affects image - Rembrandt is my favorite lighting. I will place flash 45 degree to the side pointing down on subject. This will produce partly lit face with one side properly lit and other partly in shadow with a little light triangle under models eye and nice catch lights. I'm l using a big softbox placed just outside of the frame as close to the subject as I can get away with. This is very simple one light setup easily adjusted and changed. Also it's easier to travel carrying just one light and one softbox.
Try placing light anywhere around the subject and then compare how this will affect your image. Experiment with lightning as much as you can, look on photographs of your favorite artists and try to dissect the image to figure out light placements. Catch light in the eye and shadow direction will help you to figure this out. You can learn a lot from watching movies as those are well lit. Once you can see how the scene was lit you will become much better in lighting your own portraits.