The main difference between paludarium setups and a typical vivarium is that the water section is usually much larger and is a primary focus of the build. As most want to have clear, non-murky water, a proper filtration system is required. The two best options are building an external sump or go with a canister filter. Canister filters are much easier to work with for the beginning hobbyist as they are typically less expensive than sumps and don't require nearly as much setup. I prefer to use the Cascade series as they are relatively inexpensive as canister filters go and they have on/off valves that make draining/priming easier. Typical aquarium hang on back type filters are very cumbersome with most vivaria designs and I don't recommend them for these kinds of builds.
In order to keep your water crystal clear you will need to perform periodic water changes, just like an aquarium. This will help to remove dissolved solutes in your water as they stay behind when the water evaporates. In many cases large volumes of activated carbon will be needed in your filter. The tea colored tannins leached from wood, peatmoss, and soil will tint your water brown as they build up. The activated carbon will act as a sponge and bind the tannins and other organic acids, trapping them in the filter. The more water movement and carbon you use, the longer the time between water changes. Eventually your carbon will become saturated, and you will need to replace it. What I have found works well is to purchase small granulated aquarium carbon and put it into pantyhose tied off. This will keep it from getting everywhere in your filter, but still allows water to permeate through your media. Be sure to rinse the carbon BEFORE use to prevent it from mucking up your water.
As with any other aquarium, aspects like the nitrogen cycle, pH, TDS, and chlorine removal will need to be properly addressed. In most cases your water pH will be slightly low due to the organic acids from the soil and your nitrate/nitrite levels will be variable depending on the plant/animal/biological filtration volume you have. These aspects can be adjusted by using conventional planted aquarium techniques/products.
Having the right kind of soil will make a difference in how your system performs. While it is possible to section off the soil from the water, it is very unlikely that this will remain the case throughout the lifetime of your tank, especially with semi-aquatic animals coming in/out of the water. So using a good quality low organic soil can help you keep your water clear.
There are number of different inorganic aquarium plant soils available. The most common commercially available paludarium and planted aquarium soils are small latterite or fluorite clay granules. These clays have a high cation exchange capacity, based on the water pH, and are capable of binding nutrients to themselves. By use of this soil and proper aquatic plant fertilizers you can properly grow your plants without the need of true "soil". There are a number of different products out there, but for the most part they are all about the same, with a few minor differences.
Riparium Supply carries a good quality substrate that works well for these kinds of systems. One advantage of using their product is that it has been washed to help remove the massive amount of colloid particulates that are in these raw soils. It takes me about a half hour worth of washing to remove most of these when I've use unwashed soils. If you don't wash it, the microscopic clay granules will mud up your water like chocolate milk for at least a week.