When within a contact record, under the Contact Overview menu click Activities.
By default you will see the contact's open activities, but you can click on Completed Activities in the Activity Views box to the right to see a list of their completed activities:
You can then right-click the Completed Activity you wanted to work with to see the below options:
Clicking View Completed Activity will open up a dialog displaying all of the activity's details.
Clicking Restore Activity will change the activity from Completed to Open, placing it back in the Open Activities for the contact.