In case you do not see the "Export to..." button it means that you do not have the permission to export. Please contact the administrator of your account to assign more permissions. 

Easily export upcoming and completed tasks, meetings, custom activities (all calendar activities) in the standard CSV file format from the Organizer. The history of the previous interactions with the particular customer or lead and upcoming tasks are not included in the Leads, Companies or People export file. 

1. Navigate to the Organizer section.

2. Enable the list view.

3. Mark the activities you want to export. To narrow the list - use the filter. 

4. Click the Export to ... > Comma-separated values (.csv) button which is located on top of the activities list.