What exact chemical reaction takes place when milk turns "sour"?

Answer 1

Milk, due to presence of easily usable carbohydrates (lactose), fat, protein and high nutritional value, provides an ideal environment for microbial spoilage.
Proteolysis and putrefaction are typical results of microbial spoilage of such high protein materials. Milk undergoes a predictable four-step succession during spoilage, acid production by Lactococcus lactis.
Lactis is followed by additional acid production associated with the growth of the more acid tolerant organism such as Lactobacillus.
At this point yeasts and moulds become dominant and degrade the accumulated lactic acid and the acidity gradually decreases.
Eventually protein-digesting bacteria become active, resulting in a putrid odour and bitter flavour. The milk, originally opaque, can eventually become clear.
http://www.hindu.com/seta/2006/01/05/stories/2006010500251700.htm

Answer 2

Lactic acid is produced by the fermentation of lactose (milk sugar). You can make this happen by adding lactobacillus, as in commercial yoghurt production. The milk then curdles because the acid neutralises negative charges on the surface of proteins, so that they no longer repel each other electrostatically, and stick together.