A long tap--touching and holding on the screen--will trigger the context menu for what is tapped on.
Links: Open in a new tab, copy, share, or add it to your bookmarks.
Images: Copy, share, or save the image to your device.
Bookmark links: Open in a new tab, share, edit how it appears in your list, remove it, or add it to your homescreen.
History links: Open in a new tab, share, remove, or add it to your homescreen.
Text: Long tap on text to select that word; you can then use the orange indicators on either side of the word to highlight more text if you like. Long tap on the highlighted text to copy, share, or to select all the text on the page.
Web Address: Share, subscribe or add a page to your Home Screen. If a site has its own search that follows OpenSearch standards, you'll have the option to add that site as a search engine. This allows you to search within that site directly from your search bar.
Navigating the Awesome Screen
The Awesome Screen shows you tabs at the top for Top Sites, Bookmarks, and History. You can tap on each of these to move to that tab.
For Android 4.1 Jelly Bean and up: You can also swipe left and right on the Awesome Screen to flip through the three tabs.