Contacts can be exported from any contact listing such as search results or the Organisation page Contacts tab.
To perform an action you must select at least one contact using the checkboxes on the left side of the grid, then an action from the dropdown. (Note: all records can be selected by clicking the the checkbox in the header row)
If you want to include custom fields in your export or need to search for specific records, you can use the advanced search which has extra filter and column options.
For more information about the grid actions menu and the advanced search, please see these articles