Today's video can be viewed (here) and gives an excellent introduction to speed-lights.
The video covers:
• what is a speed-light,
• hot-shoes (the flash mounting with several electrical pins you find on the top of most cameras, and cold-shoes,
• on-camera and off-camera flash,
• flash control modes (TTL which means Through The Lens metering which automatically sets the flash power level, manual control of the light output, and stroboscopic flash where a series of light pulses are generated),
• "normal", and HSS (High Speed Synch) where the flash pulses very rapidly allowing higher camera shutter speeds to be used,
• first and second curtain synch which determines whether the flash fires as the camera shutter opens or when it is about to close,
• zooming the flash to control how wide a beam of light is produced,
• tilting the flash.
One comment I'd make is that many photographers use third party speed-lights, these being considerably cheaper than those offered by the major camera brands such as Canon, Nikon, etc. Personally, I use Godox speed-lights. If you want to use TTL metering you'll have to use the light designed for that brand, whereas if you intend to stick to manual exposure control cheaper generic flashes are available.
The video doesn't say much about the decision of whether to use TTL or manual control. Many professional portrait photographers use manual mode: if you do you can be sure that a sequence of images have all been exposed to the same amount of light, and if you're not pushed for time you're not going to be bothered by the extra set up time manually adjusting the exposure. However, a wedding photographer, for example, who has to move quickly from shot to shot and work with widely changing light levels, might well choose to use TTL.
The other thing you're going to have to think about if you're going to use speed-lights is how they are placed in position and how they communicate with the camera. As shown in the video you can mount the speed-light directly on the hot-shoe of the camera. That can be very convenient and communication occurs automatically with the camera through the hot-shoe. This would be useful if you were covering a party! However, since the light will be parallel to the camera/subject axis the lighting will be very flat with little hint that the subject(s) are three dimensional objects.
Alternatively, you can place the speed-light off-camera for better results. Most speed-lights come with a little cold-shoe stand so the speed-light can be placed on some convenient surface. For better control the speed-light can be attached to a light-stand using a special bracket. There are several types you can purchase. I use one that has a Bowens-type mount for easy fixing of a variety of light modifiers (soft-boxes, umbrellas etc). I initially bought one by Neewer but found I couldn't mount the flash vertically, so I've now gone for the Godox S2 that does allow that (it should be okay for other brands of speed-light too). If you do want to mount the flash on the camera for convenience but off-axis you can purchase a special bracket for this.
Whatever method you use you will have to decide how the camera communicates with the speed-light. One way is to use a special cable with a hot-shoe at one end. Alternatively, if your camera has a built-in flash you can use that at low power to optically trigger your speed-light. You have to maintain line of sight between the camera and the speed-light though. For predictable operation I always use radio triggering. You might have to buy additional send and receive radio triggers when purchasing cheap third party speed-lights but even relatively cheap speed-lights from the likes of Godox can have the receive trigger built in. This avoids one extra bit of kit. You will find that the send transmitter that fits on the camera hot-shoe will allow manual control of the flash as shown in the video.