When a corporation makes a profit, it will often have to pay corporation tax on those profits. The rate will depend on the jurisdiction where the profit is made.
If it uses its after tax profits to pay out dividends then the shareholder may have to pay tax on those dividends as well, meaning that the profit is taxed twice. Some countries, such as Australia, give the shareholder a credit (franking credit) when the corporation tax is paid so this double tax is avoided. This, however, is not the case in the United States.
If you are a US tax resident and your dividends are "qualified" then your federal tax rates on dividends will be nothing if your income is in the 10-15% tax brackets, the rate will be 15% if your income is in the 15%-39.6% tax bracket, and your rate will be 20% if you are in the 39.6% tax bracket.
You may also need to pay a 3.8% medicare surcharge and state taxes on top. Unqualified dividends are taxed at your ordinary income tax rate.
For your dividends to be qualified, which gives you more favorable tax treatment, they need to meet certain criteria. Firstly there is a holding period. You need to have held the (common) stock for more than 60 days during the 121 day period that starts 60 days before the ex-dividend date.
Also for the dividend to be qualified, the dividend must be paid by a US corporation or by a foreign corporation that trades on a major US exchange (including ADRs) or from a corporation incorporated in a possession of the United States.
For more information, please have a look at the IRS site at: www.irs.gov/publications/p17/ch08.html#en_US_2015_publink1000171584
If you are eligible then you should look to use your tax shelters as much as possible.
These have different rules but essentially allow you to build up your dividends and capital gains tax free whilst they are in the account. Please see our page on tax advantaged accounts for more information.
You may have to pay state taxes as well as federal taxes. The rate depends on your income level and where you live. If you live in California (as of 2014), the top state rate is 13.3% where as in Alaska, Florida, Nevada, South Dakota, Texas, Washington or Wyoming there is zero state tax on dividends. The full list can be found at http://taxfoundation.org/article/united-states-high-tax-burden-personal-dividend-income