The dividend quoted on a site like the one you linked to on Yahoo shows what 1 investor owning 1 share received from the company. It is not adjusted at all for taxes. (Actually some dividend quotes are adjusted but not for taxes... see below.)
It is not adjusted because most dividends are taxed as ordinary income. This means different rates for different people, and so for simplicity's sake the quotes just show what an investor would be paid.
You're responsible for calculating and paying your own taxes.
From the IRS website:
Ordinary (taxable) dividends are the most common type of distribution from a corporation or a mutual fund. They are paid out of earnings and profits and are ordinary income to you. This means they are not capital gains. You can assume that any dividend you receive on common or preferred stock is an ordinary dividend unless the paying corporation or mutual fund tells you otherwise. Ordinary dividends will be shown in box 1a of the Form 1099-DIV you receive.
Now my disclaimer... what you see on a normal stock quote for dividend in Yahoo or Google Finance is adjusted. (Like here for GE.) Many corporations actually pay out quarterly dividends. So the number shown for a dividend will be the most recent quarterly dividend [times] 4 quarters. To find out what you would receive as an actual payment, you would need to divide GE's current $0.76 dividend by 4 quarters... $0.19. So you would receive that amount for each share of stock you owned in GE.