To export, your admin must turn on Can export data for your user. See Access permission: Export.
Click Sales & CRM → Companies & contacts, click Contacts at the top of the list, and click the box next to NAME:
This brings up options including Export option:
Click Export. In Export fields, choose the fields to include and click Export.
When the file is ready, your notifications show Contact export done. Click click to download next to it to get the file.