How are split-underwater photographs made?
What equipment is needed? Does it exist for various types of cameras?
Bonus for hints on how to use the said equipment.
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This should help - it's an article written by National Geographic's David Doubilet all about getting split shots.
The same equipment that is used for underwater photography will work. You simply put a portion of the shutter above and a portion of the shutter below. You can refine it a little more in post if you want by taking one photo above, one below and one in between (that way you can independently adjust the white balancing between the top and bottom when taking the images.)
Some companies, such as SeaLife, make cameras dedicated for underwater use. GoPro also has an enclosure that can be used for this purpose though the small lens could make a shot like this difficult and you would need a screen with applicable underwater enclosure to be able to have any hope of composing the shot.
There are also full size underwater enclosures for DSLRs (From companies like Ikelite, Equinox or Aquatica) but they tend to be VERY expensive (like in the neighborhood of $1,500 to $3,500.) They will produce the overall best result, but are cost prohibitive for most people unless they want to do underwater photography as well.
As far as lens ports go for an underwater enclosure, it would depend on what kind of line you wanted from the transition between water and air. A flat port will give you a straight line but more distortion underwater due to the way light bends when going from water to air. A domed port will give you less distortion underwater, but will likely distort the line made by the water some unless you are careful to line it up right in the middle of the dome (due to the curvature of the dome).
A water resistant camera bag is also a "low" cost option, but is still around $100 to $150 for one that I would trust. It also is only good for a few feet usually, so be sure to be careful with it. Water pressure increases extremely fast.