The standard approach to making sea salt is to evaporate the seawater in salt ponds over a period of months to years. This time period is determined by the depth of the salt layer you want to end up with, the concentration of salt in the water (35 g/ℓ), the enthalpy of vaporization of water (2.26 MJ/kg), and the terrestrial solar constant — the irradiance from the sun at the surface of the Earth. (Or, really, its average over time, filtered through the atmosphere and clouds — “mean insolation”. Peak terrestrial solar irradiance is typically about 1000W/m² but mean insolation at temperate latitudes is only about 180–280 W/m².)
(A small additional amount of heat is also added by air as it blows over the water, bringing in some solar heat from the surrounding area.)
However, the typical practice is actually to move the brine to smaller pools once it becomes more concentrated, thus evaporating most of the water over a large-area solar collector, then piling up the salt.
The vapor pressure of the water is dependent on the salinity; pure water will only condense at a relative humidity of 100% (by definition), but in the final stages, where the salt solution is saturated (359 g/ℓ) and salt begins to crystallize, the equilibrium favors condensation above 75.5% relative humidity (at 0°, slightly increasing with temperature). So heating the air somewhat may be necessary for the final stages of evaporation, to keep them from running backwards.
In theory, you should be able to adapt this progressive concentration to a continuous-flow process with a very large number of “ponds” and a very small amount of water, thus producing a continuous flow of salt very rapidly from seawater.
While the sun is shining at 1000W/m², water evaporates at 442μℓ/m²/second, producing salt (if the process gets that far) at 15.5 mg/m²/s. Given 4m² of solar collectors, this could give you 62 mg/s of salt, or a kilogram or two of salt per day, depending on how much the sun shines. If your collectors are merely water ponds 10mm deep, the collector contains 40 liters of water at any given time, which means that any given parcel of water on its way through the system will take about 6 hours to evaporate completely.
Possibly a more interesting approach is to use reflective solar concentrators to collect sunlight over a much larger area than the area actually covered in water. For example, if you could achieve three suns of concentration, water could pass through the system in only 2 hours, and as a bonus, you could heat it to a high enough temperature (up to 209°) to sterilize it as it entered, minimizing biofouling problems.