When you access a contact record in Redtail, you'll notice new menu items in your Left Menu Bar underneath Contacts (these menu items only appear when within a contact record):
After clicking Activities from the menu, you will see your contact's Open Activities (the timeframe of Open Activities on display will be based upon whatever filter dates you used when last viewing a contact's Activities page):
Note that the Subject of an Activity is a link which will open up the Activity Details for you to update, complete or delete.
Also, the Actions menu to the left of the Date for an activity provides you with several other options regarding the activity:
Above your Open Activities, you'll see menu options for Filter Dates (change the date range of Open Activities you are viewing), Activity Options (Complete, Reassign, Reschedule, Rollover or Delete), Show Completed, and Add a new Activity: