add image and other text to header via functions.php

I have searched as best I can for information on how to encode a child functions file.

I would prefer to do as much customization as possible using the child’s functions.php and the child’s stylesheet. The whole reason that I’m making this switch is that the theme I created myself, using WordPress codex, suddenly and inexplicably threw a blank white page a couple of days ago. I do not understand coding well enough to be able to find the problem. It seems essential that because of my less than skilled PHP coding skills, I want to use any updates that appear on twentytwelve to keep the inner workings of my wordpress as safe as possible from marauders.

I do understand how to add an image via the stylesheet but do not know how to resize it within the css. Can someone point me to a page on how to do that?

Thank you.

-E Morris, etherwork dot net slash blog ? purposely left unlinked in attempt to keep spammers at bay (no more bruteforce attacks for me please….)