Adding extra widget areas

I goofed (again) and posted in the wrong forum – I’d repost here, but I got in trouble last time. I’m wondering how to create a widgetized footer in twenty twelve. Here’s my screw up post in twenty ten: https://www.ads-software.com/support/topic/widgetizing-the-header-and-footer?replies=1

[ Moderator note: You could have copied the whole other post into this thread as I’ve done now. ]

I’d like to add a widgeted section to the header (I’m using a logo / masthead image, and have made the clickable title and tag line display:none) where I can add the client’s social icons.

I’d also like to make a widgeted footer area with three columns.

I’ve been reading this file: https://codex.www.ads-software.com/Widgetizing_Themes but I’m not sure if the ‘sidebar’ verbiage applies. How do I use this information for the header and footer areas?

The site is under development and not public, but here are screenshots:

https://www.elevensixty.com/footer.png
https://www.elevensixty.com/top-corner.png (corner of the header image)