Scroll down a bit to the "Search History" section, and then click "View And Clear Search History" button. This opens the "Activity History" tab of your dashboard, and puts the focus on your past searches. If what you want to do is clear your entire search history, you can just click the "Clear Activity" link at the top right of your search list.

To delete your entire browsing history, select from "the beginning of time" in the drop-down box at the top of the screen and check the "Browsing history" option. You can also choose to clear other private data from here, including your download history, cookies, and browser cache.