Thanks - for flash, there are sort of 2 levels in my mind (heck, maybe three since I like to mix flash with ambient or hot lights sometimes).
Most basic is a flash stuck on the camera, which does the job but doesn't often give you the most aesthetically pleasing results. Then there's flash off-camera, where you get into far more control.
For off-camera, you can use regular hot-shoe flashes with a stand adapter, and there are adapters that let you sue reflectors or soft boxes. But you may not get much manual control that way, like you may only have a couple power levels to choose from.
Next up is a strobe designed for off-camera use - that could be a monolight (the bulb and capacitor and controls are all on the actual lighting unit so you only have a power cable, and many of those have multiple power levels you can control with a knob); or a pack and head system, where there's a box that sits on the floor that powers separate cabled heads that just have the flash tube and usually a modeling light. The purpose of the modeling light is to illuminate the subject just as the flash would (with much less power of course) using a continuous light bulb. So if you stick a reflector or a grid or a softbox on the flash, you can see its effect and aim it and so on.
Flash usually requires some sort of diffusion, or control like grids or barn doors. Softboxes are sort of "tents" that mount on the flash with a diffusion fabric face, but the sides keep light from spilling everywhere (vs. an umbrella that fills the whole space with some light). Many softboxes can also accept a fabric grid or "eggcrate" to keep the light soft but more directional. Each flash manufacturer will use a special mount that accessories work with - the Bowens mount is used on many consumer-ish grade strobes, Speedotron, Novatron, Norman, etc. all have proprietary mounts. You can also control the flash by shooting it through fabric (just a handing sheet of diffusion, or a frame setup) or bouncing it off walls or big sheets of white foamcore. And you can get monolights or power packs in a wide range of power levels. Power packs usually have outlets for 2 or 3 or more heads, and you can control light output to separate heads, sometimes with dedicated controls or by choosing different output connectors that have different power levels. Sometimes you can't get the power low enough so you stick another head on the pack and aim it into another room to "bleed off" power.
Generally you want some sort of radio transmitter vs. a cable from your camera, and if you have multiple flashes going, you may need extra receivers; some packs and monolights have built-in optical slaves that sense the pulse of a flash and trigger the unit, and you can also get slaves that plug into the unit's sync connector - with a low-key setup with very controlled lighting, sometimes you have to stick a slave on a cable and get it close to the set.
To measure exposure, a flash meter is pretty necessary, and back in the day we'd use polaroid backs for complex setups. Nowadays, a DSLR set to manual with a similar focal length lens is a good way to dial in a lighting setup. The other thing that can get out of hand is stands and grip... you need stands for each flash unit or head, often stands to hold diffusion or cards to cut and shape the light, boom arms, grip heads, clamps, and there are tons of specialized things - like,
this black mesh frame that cuts the light by a set amount, which you can use to down down a bright spot or cast a specific shadow - it needs a stand with (usually) a boom arm and a grip head to hold it in place. And then things like softboxes and
grids that fit your specific mount.
I'm sure there are books out there, but these days it's youtube videos and blogs by people who are good at (or so-so or even terrible at) lighting with strobes. It's one of those endless possibilities things, but also something that your brain may connect to quickly, and you can build up gear over time as needed. You might start a thread here asking for books and specific web sites people have used? Good luck though, the power and control to take an idea to an image is pretty awesome.
