While in the web browser, touch and hold your Stylus on your GamePad screen, then drag the tip of your Stylus over any text and it will begin to highlight words in blue and also the "Copy" option will appear at the bottom of the screen and you then touch the Copy icon.
Then when you have entered a text box, tap that area with the Stylus and the Wii U typewriter will now appear and it'll have the "Paste" icon on it to paste whatever you previously highlighted in blue.