If the soil contains excess salts (whether sodium salts or other kinds), plants typically grow slowly or stop growing completely; they often show yellow leaves as well. Sometimes you'll even see a white, salty deposit on the soil surface.
Salty soils are most often found where rainfall is fairly low and in oceanside regions where salt water has entered the soil or salt spray has been absorbed by plants and soil. But even in inland areas with adequate rainfall, salt can build up in the soil if drainage is poor. Heavy use of fertilizers can also lead to salty soil, as can the salting of roads in winter to dissolve ice.
The way to deal with salty soil depends on what's causing the problem. If you live near the ocean, choose salt-tolerant plants and use windbreaks to protect your garden from sea spray. If poor drainage is the problem, correct it. If you suspect that over-enthusiastic fertilizing is to blame, consider replacing heavy feeders with plants that require less fertilizer, and choose organic fertilizers that release lower amounts of nutrients at a slower rate.
In low-rainfall regions, water thoroughly and deeply to help leach the salt below the plants' root zone. You may need to increase water by as much as 50% in a season to leach out the salt; you can either forego planting entirely that season or choose only plants that tolerate ample water. One caution here: if the excess salt is in fact sodium, it will bond to the soil particles and cannot be washed away with water alone. Gypsum must be added as well. Experts can look at the whitish salt crust on soil and tell at once if it is a sodium salt, but most home gardeners will need to send a sample to a laboratory for identification.
If soil is highly salty, the only successful way to garden may be in high raised beds filled with healthy, well-amended topsoil.