A semi-aquatic vivarium is a tank with a land and a water portion. The water is usually 50% or more of the tank and of sufficient depth to allow the animal to swim. They come in many different forms. A paludarium is another term for a semi-aquatic tank. They combine the elements of a terrarium and an aquarium and may copy a river, a mangrove forest, a swamp/marsh, or a pond.
Animals they may like these environments include newts, fish, sirens, mud puppies, snakes, crabs, lizards or frogs. Turtles also inhabit such an environment but their tanks must be pretty bare bones since they are large, heavy, and will eat/uproot plants. Mixing species is generally not recommended unless you know they will not interfere with each other. General rules to follow are to only mix non aggressive animals that will mostly stay to separate parts of the tank, and to not mix a predator with a possible prey item (unless feeding is the goal).
There are as many ways to set up a paludarium as there are animals and plants to use, but there are a few basic design. You can have the land part just be a background wall with plants attached in which case your paludarium will be no more than a half filled aquarium. It can be shallow water with emergent rocks and wood (very simple). It can be a divided tank where a piece of glass or plexi-glass divides the tank into a water and land area. The land area can slope into the water like the edge of a pond (very naturalistic). The land area can be a shelf that juts out into the water (a cross between the wall and slope systems). Finally there could be no “land” at all and you could simply have plants growing out of the water (like mangroves).
Whatever setup you choose live plants will make the tank look better and they will help clean the tank. A filter will also be required to circulate the water and filter out wastes. You could possibly consider working the filter into a water feature like a waterfall.
The land part can be made of foam, cork bark, gravel, rocks, or rot resistant wood. Note that wood must be soaked in water before use to clean it and leach out some of the tannins. Too much tannins from the wood will make the water too dark to see the animals. some tannins in the water will not hurt your animals, though (tadpoles actually benefit from them). The color tannins impart can also add interest to the tank. The substrate in the water part may be gravel or sand. When choosing plants look for tropical varieties well suited to growing in tanks and under wet conditions (the exception would be plants that are placed far from the water like tillandsias). Some plants to use include pothos, duckweed, dwarf papyrus, java moss, arrowhead, and many others.
The tank below was made for eastern newts. It is an emergent style with rocks coming out of the water and a piece of wood laying across them. The tank has only aquatic plants (came in those little packs of dry bulbs you can get at pet shops for aquariums). Notice the color of the water from the wood tannins. The newts breed in his tank and some of the larvae grew up in it. There is a filter in the back that forced water over part of the wood. Partial water changes were done with a turkey baster so as not to disturb the tank. I seeded this tank with pond water so the water had some micro fauna that the newt larvae ate.