Creator of the Volunteer Event can sign up another person to be a volunteer. Just follow these steps. 

1. Click on the Class name in the left navigation tray 
2. Click on Signups in the Updates tab 
3. Click on the Volunteer Event you have created
4. The Volunteer Event details screen is seen
5. Scroll down to see the Signups||Comments||Invitees tabs
6. To assign a parent to volunteer, click on the Sign Up icon
7. Tap Volunteer and pick the person and click Done
8. If signing up for an item, click Quantity and input number of items assigned to volunteer
9. Tap Reminder to set up a reminder for yourself from the drop-down menu
10. Type in any extra info in Comment
11. Click on the Sign Up icon
12. The person to whom the Item/ task is assigned to will be notified

For more information, check out the following articles:

Requesting Volunteers for Recurring Tasks in Class

Requesting Volunteers for My Class Event

Signing Up to Be a Volunteer

Canceling My Volunteer Sign Up

Asking a Question on a Volunteer Task

Editing a Volunteer Event