The search function on the Leads List (or Leads Tab) only searches the data displayed, so in order to search for a lead by their email address, you must first choose to display the email data field in one of your custom columns. Once you set this, enter an email address in the search box and click the search icon.
The Leads List has two custom columns - which are highlighted in a darker grey in the header row. These exist between the Name column and the Date Added column, and are also marked with a light blue asterisk icon. The first custom column defaults to "Full Address" and the second one is blank. To change the column contents, click on the asterisk icon, and then choose the data field you wish to display. You may also save this configuration as a "View" in order to quickly reference it in the future.
For example, if you wanted a representation of your Leads List showing their name and email address, make sure you start on the "All Leads" view. Then click on the asterisk icon in the first custom column ("Full Address" ) and change this to "Email" - then next to the Current View line, you will now see "Custom List" in a dropdown menu. Immediately to the right of this, click on the "Save This View" link and then name the view "Email Address List" and save.
This view will now be available at any time from your Current View dropdown menu.