Click the 'Settings' link from the left-hand menu.

Choose the 'Export Data' option from the 'Data Management' section.
You'll see options in the page to export the following types of data:
People
Companies
Opportunities
Projects
Tasks
Leads

Click the blue 'Export [record type]' button below the record type you want to export.

You will receive an email from Copper when the export is ready for download.