To make this change per Event and from within your Event, navigate to your General Event Settings. Right below the Minimum and Maximum Staff settings, you can choose whether or not to 'Collect Availability for this Event'.
To make this change at the Organization level, navigate to your Event list within your Organization and select the Events you wish to change settings for using the checkboxes along the left-hand side of the list. Once you have finalized your selection, click on the 'Take Action Button' and select 'Event Settings'.
You can use the pop-up that appears to edit multiple Event settings including the choice to 'Collect Event Availability'. Making any changes here will, in bulk, apply the changes to your selection.
If you choose to collect Availability for your Event, enable Availability in the 'Self-Signup Settings' so that Volunteers can mark their availability during the registration process.
It should be noted that any changes made to General Availability will carry down to the Event while any changes to Event Availability will not be reflected in General Availability.