While it failed to name the ways specific corporations avoided taxes, the GAO survey, based on Internal Revenue Service records, attributes the failure to three factors: tax credits, operating losses and “transfer pricing,” which means corporations internally shift taxable profits to their own subsidiaries in lower-tax nations.
Transfer pricing means a corporation “sells” its products to a subsidiary in another country at a low profit. They pay taxes on that low profit. The subsidiary then sells the product at full price.
The GAO report (PDF) has much more about how corporations avoid taxes.
It’s ironic that the GOP argues dividends should be taxed at a lower rate (or not taxed at all) because corporate income has already been taxed once. OTOH, they also argue that this tax break benefits the average American. What percentage of the average American’s income (or yours) comes from corporate dividends?