Activities can be viewed on Activity page under Leads and Opportunities tab.
There are two ways to view the activity of a particular contact.
1. Search Bar - This option will search for any data that contains your query "Contains" whether it is exact or not.
2. Filtering - you can easily customise the filter view via:
Contact Full Name
After searching for a certain contact, clicking the "To Do" will direct you to the Call Log for that Activity. There you can complete the Activity by marking it as successful. You can also create future "follow on" to be completed in the future.