Titles can be removed from the basket in a number of ways.
On the search results page you can remove individual titles by un-checking the box beside the search result or by clicking Remove from basket.

On the search results page you can remove titles in batch by un-checking the select all box at the top of the results or clicking Clear basket.

Titles can also be removed individually by clicking Remove from basket on the title details page.

When viewing a basket, you can select the titles you wish to remove and use the Delete button in the basket view.

The entire basket can be cleared by slecting the Clear Basket action from the basket icon drop down menu.

The entire basket can also be cleared by checking the box for Clear entire basket when actions complete before performing an action when viewing a basket.

Additionally, the contents of the basket are cleared when you log out of your account.