How do I show which parenthesis matches the one I'm looking at?

If you're looking at a right parenthesis (or brace or bracket) you can delete it and reinsert it. Emacs will blink the cursor on the matching parenthesis.

M-C-f (forward-sexp) and M-C-b (backward-sexp) will skip over balanced parentheses, so you can see which parentheses match. (You can train it to skip over balanced brackets and braces at the same time by modifying the syntax table.)

Here is some Emacs Lisp that will make the % key show the matching parenthesis, like in vi. In addition, if the cursor isn't over a parenthesis, it simply inserts a % like normal.

  ;; By an unknown contributor

  (global-set-key "%" 'match-paren)

  (defun match-paren (arg)
    "Go to the matching parenthesis if on parenthesis otherwise insert %."
    (interactive "p")
    (cond ((looking-at "\\s\(") (forward-list 1) (backward-char 1))
          ((looking-at "\\s\)") (forward-char 1) (backward-list 1))
          (t (self-insert-command (or arg 1)))))