The report published by the Permanent Subcommittee on Investigations detailing Apple's strategies is a great read on its own.
The report gives an inside look on Apple's absolutely genius tax avoidance strategies.
Apple uses a variety of offshore structures and arrangements to shift billions of dollars from the United States to Ireland.
The U.S. corporate tax rate is 35%, while Apple said it has negotiated a special corporate tax rate in Ireland of less than 2%*.
(The 2% rate statement has proven controversial, see below for details)
Apple has found the secret to not paying taxes. You just avoid taxes by not declaring a tax residency for the company that oversees the entirety of your international income.