In Emacs how do I edit multiple points at once?

Emacs Rocks! describes mark-multiple, which does what you want. (Here's their video introduction.)

EDIT: @Lifton points out it has been superceded by multiple-cursors.

In addition to Juancho's answer, I've used Steve Yegge's multi-select for your purpose. Example usage (the first example will provide what I think you want):

 C-u C-M-m w foo <RET> <RET>
  - inserts/prepends "foo" to every multi-selection (you can also append or replace text)

 C-u -1 C-M-m r <pre>\(\w+\).+\s-+\(.+\)</pre>
  - selects first and last word of the contents every <pre> tag
    (provided the contents don't span multiple lines)

 C-M-m x M-x upcase-region
  - converts all multi-selections in buffer to uppercase

 C-u M-w C-q C-j --- C-q C-j <RET>
  - saves all multi-selections to kill-ring as a single item,
    with selections separated by "---" on a line by itself