"what happens if you drink a large amount of water without ingesting anything salty? "

Depends on what you consider "Large". Usually what we consider large amounts, would just make us urinate as it is not water that we need and so would filter it out. 

However if you were to say ingest such an amount that it has become toxic, you run the risk of a very dangerous condition called Hyperhydration or Water Intoxication. Under most normal circumstances water and salt are present in cells and the blood. If you remember; water travels through osmosis, or from a higher to lower concentration across a semipermeable membrane. Salt helps to maintain the concentration. However if you drink so much water that it would be considered "toxic" the water that would eventually find it's way into your blood would try to balance with the cells, which begin to absorb so much water that they swell, therefore causing swelling to the body's tissues and organs.

The dangerous bit is when the brain begins to swell. Symptoms such as headache, personality changes, changes in behavior, confusion, irritability, and drowsiness. These are sometimes followed by difficulty breathing during exertion, muscle weakness & pain, twitching, or cramping, nausea, vomiting, and thirst, begin to manifest. The dangerous bit is when the swelling compresses the brain to such a degree it crushes the brain stem and herniates through the foramen magnum. The brain stem or Medulla Oblangata is responsible for the processes keeping you alive, and if it's crushed your heart rate, blood pressure, and breathing will become compromised, a recognizable feature we EMT's look out for called Cushing's Triad.  This is mostly irreversible and will lead to neurogenic shock, coma, and then death.

The important lesson, is to always take thing in moderation.