How to set dye with clothes just bought

The problem with this question is that you don't know what dye was used, when you buy clothing. A treatment that will help set acid dyes will tend to strip off  fiber reactive dyes, while the carbonate that will set fiber reactive dyes won't do any good for union dyes. You must match such chemical treatments to the exact dye type that was used, for acceptable results. Furthermore, such treatments are best used at the time of dyeing, rather than much later.
 
Vinegar is not the answer! 
Many people who know nothing about this subject recommend 'setting' dye in cotton clothing with vinegar. In fact, vinegar can do nothing useful for cotton dyes. Vinegar will help set some acid dyes,but only if applied while it is gradually heated to a simmer (generally in the presence of salt), solely in cases in which this necessary part of acid dyeing was omitted; acid dyes are used on silk, wool, or nylon, but never cotton.
 
Salt won't do it, either. 
Salt can be useful in dyeing, by encouraging the fiber not to repel the dye, or by making the dye less soluble, but it will not itself  fix the dye to the fiber. Washing your garment with salt won't hurt it, but it also will not help. The extra washing will help to remove the dye only because it's another run through the washer, which can help to remove excess dye.
 
Washing Out Excess Dye.
In some cases, the clothing may be dyed correctly, and also have excess dye in it. This is true of fabrics dyed with fiber reactive dye that have not been washed adequately. In such cases, the simplest solution is to simply go ahead and wash -repeatedly. The test for whether all excess dye has been removed is simple:  dampen the dyed item and iron it dry, while pressing it against a bit of white fabric. If the undyed fabric stays white, the dyed fabric (or yarn) can be trusted. Normally, the most popular fiber reactive dye, Procion MX type dye, requires at least one washing in cold water (without detergent, unless it's Synthrapol), followed by at least two washings in hot water, WITH detergent, to remove the last bits of unattached dye. Hot water is much more efficient than warm water at removing the last bits of unattached dye.