Hi Sophia - and welcome to Wetpixel
That's quite a question as it depends on so many parameters and personal preferences. But for starters - you need:
- A camera: DSLR, compact or mirrorless
- Lenses: generally this amounts to two of them: macro for shooting little critters and wide-angle. Lens choices underwater are much more extreme than are used for land photography.
- A housing: to fit the camera body in - usually the most expensive bit of the setup.
- A Port or ports to house the lens. The port attaches to the housing in a similar way to the lens fits on to the camera. It's essentially a tube with glass at the business end which bayonets on to the housing. A macro port has flat glass at the end; a wide-angle port has glass which is dome shaped and this kind of port is usually referred to as a "dome port".
- Strobes - (flash guns as they are called above water): specialist ones for underwater. You can start with one and, when you are ready, can buy and use a second one to give more balanced and flexible lighting setups.
- Either electric cables or fibre optic cables to fire the strobes
- Arms/clamps to attach the strobes to the housing and to allow you to move the strobes around to light whatever is your subject.
After that there are myriad aids and bits and bobs to help make systems more buoyant, provide better focussing light, help prevent potential leaks etc. The "investment": you can put into a system is endless.
I'd suggest getting your hands on a couple of books which will explain things in a bit more detail: "The Underwater Photographer" by Martin Edge and/or "Underwater Photography Masterclass" by Alex Mustard. Both are available through Amazon and will walk you through the basics.
So much depends on how serious you are, how much you want to spend, how much you dive and how experienced you are. Unfortunately most routes are expensive and the loss on moving from one level of system to the next up can be quite hefty.
if you are used to using a DSLR type camera or compact camera above water we might be able to give you a better steer.
Hope that helps a bit!