There are three major sources of salt, two originating from saltwater, which are evaporation and desalination, the odd one out's source being a mine that produces table and rock salt. In the 1800s, a high quality salt was produced from water commercially simply by boiling it, amongst other techniques, such as those involving a graduation house, which are no longer economically feasible.
Sea salt, not to be confused with table salt, is extracted from the sea as you might think; using few devices in a straightforward process, sea water is gathered, usually by short canals along the coast, and is evaporated by the sun and wind in what is known as a saline, salt garden, or basin, leaving behind coarse crystals with various trace amounts of minerals alongside the sodium chloride.
All evaporation basins are connected, each one being shallower and more spacious that the last, making a subsequential string of more saline water, seperated by dikes, as they progress through the system. Once the crystals are exposed, special tractors equipped with a sort of scraper harvest them. While some sites are outdoors, to completely process the water so all the minerals can be obtained takes years this way, requiring an indoor facility, unless it hasn't rained in your area for half a decade. The concentrated salt water, known as brine, can be heated in conjunction with evaporation to speed up the process, much like in salt pans.
An older and less industrious method of salt extraction from salt water involves it being placed in a shallow, open pan, made of iron or clay. They function much the same way as ponds, except a pan is indoors so it is unaffected by the wind and uses a heatsource other than the sun to bring on the evaporation, such as a fire. Salt was extracted this way thousands of years ago when the pans were made from a ceramic known as briquetage made specifically for evaporation or lead. These were heated by fires, the transition to coal from wood as an energy source made briquetage obsolete.
Table salt is most commonly mined, but it can also come from water through the process of desalination, which primary objective is to purify water so it is fit for humans, the salt can either be discarded or kept. Flash distillation, reverse osmosis, and the boiling of water at lower pressures, vacuum distillation, are predominately used in desalination.