Salt (sodium chloride, specifically) is important in using many types of dyes. Exactly how it should (or should not) be used depends on the specific type of dye in question. When using salt, always follow the recommendations of the dye manufacturer, unless you know better.
Contrary to some old wives' tales, salt is not a dye fixative and does nothing to make dye more permanent; however, it aids in the dyeing process by helping to drive the dye onto the fiber, out of solution, so that it is in the right place for any bonding to the fiber to occur.
What kind of salt should be used
Most recipes call for ordinary non-iodized table salt (sodium chloride). The small amount of iodine in iodized salt will probably have no effect, but it's easy to find non-iodized salt, and then you don't have to worry about it. The other ingredients often found added to salt, such as the sodium silicoaluminate often used to promote free flowing, should have no discernable effect, positive or negative.
I usually get pure pickling salt from the grocery store, in 4-pound boxes. Some people prefer koshering salt. I say, get whatever is cheapest and most convenient. Finer grains of salt will dissolve more easily than larger grains. Note that different shapes of the grains cause different salts to have different volumes per weight. Replace one cup of ordinary plain granulated salt with one and a quarter cups of Morton's Coarse Kosher Salt or two cups of Diamond Crystal Kosher Salt, in order to obtain the same weight of salt.
A few recipes call for Glauber's salt, which is sodium sulfate, instead. You can buy Glauber's salt from your dye supplier (see Sources for Dyeing Supplies). Procion MX turquoise is said to dye more intensely with Glauber's salt than with sodium chloride. However, the vast majority of complaints about turquoise coming out too pale, among MX dye users, are due to low temperatures; Procion type turquoise MX-G must be at least 70° Fahrenheit, or 21° C, and is happier at 80° or 90° Fahrenheit {27-32°C) when reacting with the fiber, though it's fine to dissolve it in slightly cooler water). It usually makes much more sense to try increasing the reaction temperature than to start messing around with adding different salts, if this is your problem.
Tie Dyeing
In tie-dyeing cotton, rayon, and silk, using fiber reactive dyes such as Procion MX or Sabracron F, there is no need to use salt at all. (Other dyes will require salt, but it is best to use fiber reactive dyes, for tie-dyeing cellulose fibers such as cotton and rayon, because they are both easier to use and produce much more satisfactory results.)
Immersion or Vat dyeing with fiber reactive dye
In immersion dyeing (bucket or washing machine dyeing) cellulose fibers or silk, using fiber reactive dyes such as Procion MX or Sabracron F, salt is important in helping to drive the dye out of the vast amount of water (which is necessary for smooth, even, unstreaked dyeing) onto the fiber. Use one cup per gallon of water, or follow whatever recipe you have already. Add the salt to the water separately from the dye - dissolve the dye first in water, before adding to the tub full of salt water - because salt makes the dye less likely to dissolve in water.
Low Water Immersion Dyeing
Some dyers like to use salt in Low Water Immersion dyeing, while others do not. Some say that they get better "crystalline" markings with salt; other disagree. Experiment for yourself! It probably depends on which specific dye colors you use, how much you agitate (more agitation means less pronounced markings), and other conditions such as the temperature of your workroom, etc.
Again, be sure to dissolve the dye first without salt, as it may be impossible in the presense of the salt.
Direct dye
Direct dye is the portion of all-purpose dye, such as Rit brand dye, which dyes cotton and other cellulose fibers. (The brighter acid dye portion just washes out of these fibers, but will dye animal fibers such as wool, and also nylon.) Direct dye can also be purchased on its own, such as PRO Chemical & Dye's line of Diazol Direct dyes; this would make more sense than wasting money on a mixture of two dyes when only one will work, except that most people who are going to the trouble of ordering specific dye types vastly prefer fiber reactive dyes for cellulose fibers.
You certainly should use salt when dyeing with direct dye, following the manufacturer's instructions. It is best to start with no salt in your hot water bath of water plus fiber plus dye, then gradually add the salt, in several portions, at intervals of perhaps ten minutes.
Dyes for Protein fibers
Again, always pay strict attention to the manufacturer's instructions, unless you have better information. While recipes for direct dye application (like those for tie-dyeing) tend to omit salt, immersion dyeing with acid dyes, as well as lanaset dyes, calls for the use of regular salt (sodium chloride) or Glauber's salt (sodium sulfate decahydrate). PROchem's One Shot dyes do not call for the use of salt, presumably because they already contain it.
Vat dyes such as Indigo
Interestingly, PROchem's recipe for Indigo calls for salt in dyeing cotton, linen, rayon, and silk, but not in dyeing wool. When dyeing with Indigo and other Vat dyes, I strongly recommend paying strict attention to a good dye seller's recommendations; the chemistry of vat dyes is so unlike that of other dyes that their recipes are beyond the scope of this web site at this time.