In order to delete a session you must go into the 'Activities' tab. Under the activity you should select the 'edit sessions' button.
For the session you wish to delete you should select the 'remove' button at the end of the session row. You must then select the 'Save Sessions' button and confirm you wish to remove this session.
If the session has registered players you will be given the option to email these participants notifying them the session has been cancelled.
In order to delete an activity you must make sure you have removed all sessions from the activity you wish to delete first. Once there are no sessions associated with the activity you should see a 'Delete activity' button at the bottom right of the activity box which will delete the activity at point of click.