Here's the answer:
Change the directive
UserDir Sites
in /etc/httpd/httpd.conf
to
UserDir FolderYouWant
Note, however, that you envision accessing all your files (Documents, Pictures, etc.) that way, it won't work.
The web server runs as user 'www'. The permissions in your home folder allow other users, like 'www', to access the Sites folder, and to see the contents of your home folder, but not of the subfolders (like Documents, Pictures, Movies, etc.)
If you really want complete access to your files via the webserver, you'll want to run a separate copy of Apache that runs
as you, instead of www. This is definitely a security risk, but it's doable.
If you want to do this, do this:
1. Copy the file /etc/httpd/httpd.conf to somewhere in your home folder, e.g. in Library.
2. Edit that file, and change
every single reference to a system-wide folder (like /var/log/httpd) to somewhere in your own home folder (e.g. /Users/yourname/Library).
3. Change the port that this Apache runs on from 80 to something else, like 8080. (That's the 'Port' directive)
4. When you're all done, go to the Terminal and type:
httpd -f /Users/yourname/Library/httpd.conf
If you made all the changes correctly, it will work.
You can see
this article for a brief mention of a similar change.