Generally, editing an activity is not encouraged. There are a couple of reasons.
However, if you need to change the activity subject or description, you will have to edit the activity. For meeting activities, you may also edit it to change the time or date. For most other cases, we suggest you consider creating a follow-up activity and use the subject field to indicate you are making a correction.

Another reason you might want to edit an activity is to adjust the time, and select whether the time is billable or not.
We have added a button to the view activity screen which allows you to easily convert the time on an activity to Billable or Non-Billable.
To adjust the time, you should reconcile or approve the item which the activity is against - such as the job, issue or contract package. If the activity is against a prospect or another object, there is no reconcile screen, so if you really need to change the time, you can edit the activity.
Everyone can delete their own activities (provided they aren't locked). You need the activity delete permission to delete other's activities.
From the activity view screen, select Activity Operations > Delete Activity.