Original Source Sharan Majumdar's "The Swing of a Cricket Ball"

Original Source James Foster's page on The Science of Swing

The key to making a cricket ball swing is to cause a pressure difference between the two sides of the ball. The air pressure depends on the flow of air over each side of the ball. Swing is generated when bowlers, by accident or design, disrupt the flow of air over one side of the ball.

Normal swing

Normal swing is acheived by keeping one side of the ball polished smooth and shiny, and delivering the ball with the polished side forward, and the seam angled in the direction of desired swing. The outswinging delivery moves away from the right-handed batsman, while the inswinger moves in towards him. Normal swing is achieved by maintaining laminar boundary layer air-flow on the shiny side whilst creating turbulent flow on the seam side. These deliveries, particularly the outswinger, are the bread and butter of opening bowlers who get to use the ball while it is still new.

Reverse Swing

Reverse swing is very different to conventional swing. Although the seam is oriented in the same way as for an outswinger and the action is the same, the rough side of the ball is to the fore, and the ball moves in to the batsman like an inswinger. Reverse swing is achieved when the ball is bowled very fast. In this case the air flow will become turbulent on both sides before it reaches the seam.

Some points of interest:

Humidity: Despite being widely observed in practice, there is currently no theoretical, or experimental, evidence for humidity having any affect on the amount of swing. Humid air is less dense than dry air - although the difference is minimal - and so would be expected to induce less swing. Experiments in wind tunnels show no noticeable difference in the amount of swing between dry and humid air, and there is no measureable aerodynamic difference in the state of the ball due to moisture.

Late Swing: There are several possible explanations for late swing - where sideways movement occurs only late in the ball's flight.
i). It is an illusion. The flight path of a ball with a constant sideways-acting force applied to it is parabolic: the amount of the sideways movement naturally increases along the flight path.
ii). The ball is initially above the transition speed for turbulent flow on the shiny, non-seam side, but drops below this threshold as it deccelerates in flight, particularly after bouncing, initiating late swing.
iii). The ball rotates slightly in flight, with the seam becoming angled and thus initiating late swing.

For more details "The Swing of a Cricket Ball"

References:
Mehta, R.D., Wood, D., 1980, Aerodynamics of the cricket ball: New Scientist, 7 August, p. 442-447
Mehta, R.D., Bentley, K., Proudlove, M., and Varty, P., 1983, Factors affecting cricket ball swing: Nature, vol. 303., p. 787-788
Daish, C.B., 1972, The physics of ball games: London, English Universities Press
Mehta, R.D., Bown, W., 1994, What makes a ball swing?: Independent (?)