How do you ensure best SEO for a re-designed website?

[Madsack791]

I am re-designing a website and just wanted to clarify a couple of things about SEO.

1) Does it make a difference to Google if all the HTML files are in the root folder or are organised into sub-folders?

2) How do I get Google to recognise the new site and not try to send people to the old site or "page not found" when they search? Will re-submitting the new site to Google automatically get rid of the old links or do I have to do anything else?

Thanks for any help!
Thanks JeffE! If the new URL is the same and I keep the file names the same (as in the old files are deleted) does Google see these as completely new files, or just updates of the old ones? I assume if I change the folder structure they are recognised as different files.