I just changed the title to focus on high-speed videography, which is a much, much narrower topic than videography (and cinematography) in general.
The basics are these: due to persistence of vision, the eye can be fooled into interpreting a series of still images as if they are continuous motion at around 16 frames per second. There are a variety of reasons why people shoot at 24, 25, 30, 60, and even 120 frames per second for "normal" speed.
The premise of high-speed video recording is to capture and display temporal details that are normally too fast for human vision to really make sense of: a balloon bursting, the details of a bee's or a hummingbird's wing-beats, the flight of bullet fired from a gun.
A hummingbird flaps its wings approximately 50 times per second. If sampled at 25 fps with a 180-degree shutter (meaning 1/2 of 1/25th of a second, or 1/50th of a second), then every other wing beat would be fully blurred across the entire range of motion of the flapping. If the shutter were restricted to 18 degrees (meaning 1/500th of a second), the blur of the wing would be reduced to 1/10th the total range of the flap. Again, every other wingbeat would be imaged, and what would show up is approximately the same 1/10th of the wing beat every time. As a movie, it would look like the hummingbird was hovering due to a blurry wing that didn't really move. That's still not a very good visual explanation of what's happening.
If you want the wings to beat 2x per second, or 120 bpm, you need to slow them down by 25x (from 50 bps down to 2 bps), which, at 25fps would mean shooting 625 fps. A standard shutter angle for the perception of smooth images at any frame rate is 180 degrees, which means 1/1250th of a second.
There are various cameras that shoot at such high frame rates. Many have severe restrictions on the resolution they can provide and/or the image compression schemes they use. At the high end, a Phantom sets the pace, and records up to 1,000,000 frames per second. In the consumer world, SONY sells a camera that will do up to 960 fps (1000 fps in PAL).
Once you have sorted out what frame rate is necessary to expand the event you care about (such as how long it takes for a bullet to pass through an apple) to the time frame you want to observe (a 30 second excerpt of a pop song), you can calculate the slowdown you need, and from that also the shutter speed you will need.
Once you know your shutter speed and the camera's sensitivity, you can calculate how much light you need. If you are shooting at 1,000,000 frames per second with a 360 degree (1/1,000,000th of a second) shutter, you need a lot of light. Like 1,000x (or 10 f-stops) more light than when shooting at 1,000th of a second. Getting a bright enough light that doesn't melt your subject (or turn it to smoke), and that does not appear to flicker or wander when capturing high speed requires research. The Sun has none of these problems, but it doesn't work at night or inside a studio.
Finally, you have to worry about depth of field. When shooting things at normal speed, a focus-puller can adjust focus as the subject moves from one depth in the frame to another. Since nobody can pull focus at super-sonic speed, one must determine how much depth of field is necessary for the crucial moments of the shot, and then compose so that those crucial moments are all in focus from beginning to end.
Now, it may be that you are just interested in 48fps or 96fps, slowed down to 24fps. That's a lot less extreme than 500 fps or 1,000,000 fps. But the caveats apply: you need more lighting than when shooting at slower frame rates and shutter speeds, you need lighting that won't flicker, and you need to appreciate that it gets exponentially more difficult to track focus as your multiple of the normal frame rate increases.
