ANSI Dvorak layout:

-------------------------------------------------
| ! | @ | # | $ | % | ^ | & | * | ( | ) | [ | + |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 0 | ] | = |
-------------------------------------------------
 | " | < | > | P | Y | F | G | C | R | L | ? |
 | ' | , | . | p | y | f | g | c | r | l | / |
 ----------------------------------------------
  | A | O | E | U | I | D | H | T | N | S | _ |
  | a | o | e | u | i | d | h | t | n | s | - |
  ---------------------------------------------
   | : | Q | J | K | X | B | M | W | V | Z |
   | ; | q | j | k | x | b | m | w | v | z |
   -----------------------------------------

Dvorak with QWERTY keys (i.e., with curly braces, and the square brackets not on the same key):

---------------------------------------------------------
| ~ | ! | @ | # | $ | % | ^ | & | * | ( | ) | { | } | | |
| ` | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 0 | [ | ] | \ |
---------------------------------------------------------
     | " | < | > | P | Y | F | G | C | R | L | ? | + |
     | ' | , | . | p | y | f | g | c | r | l | / | = |
     -------------------------------------------------
      | A | O | E | U | I | D | H | T | N | S | _ |
      | a | o | e | u | i | d | h | t | n | s | - |
      ---------------------------------------------
       | : | Q | J | K | X | B | M | W | V | Z |
       | ; | q | j | k | x | b | m | w | v | z |
       -----------------------------------------

Left-handed Dvorak layout

---------------------------------------------------------
| ~ | { | } | ? | P | F | M | L | J | $ | # | @ | ! | | |
| ` | [ | ] | / | p | f | m | l | j | 4 | 3 | 2 | 1 | \ |
---------------------------------------------------------
     | : | Q | B | Y | U | R | S | O | > | ^ | % | + |
     | ; | q | b | f | u | r | s | o | . | 6 | 5 | = |
     -------------------------------------------------
      | _ | K | C | D | T | H | E | A | Z | * | & |
      | - | k | c | d | t | h | e | a | z | 8 | 7 |
      ---------------------------------------------
       | " | X | G | V | W | N | I | < | ) | ( |
       | ' | x | g | v | w | n | i | , | 0 | 9 |
       -----------------------------------------

Right-handed Dvorak layout

---------------------------------------------------------
| ~ | ! | @ | # | $ | J | L | M | F | P | ? | { | } | | |
| ` | 1 | 2 | 3 | 4 | j | l | m | f | p | / | [ | ] | \ |
---------------------------------------------------------
     | % | ^ | Q | > | O | R | S | U | Y | B | : | + |
     | 5 | 6 | q | . | o | r | s | u | y | b | ; | = |
     -------------------------------------------------
      | & | * | Z | A | E | H | T | D | C | K | _ |
      | 7 | 8 | z | a | e | h | t | d | c | k | - |
      ---------------------------------------------
       | ( | ) | X | < | I | N | W | V | G | " |
       | 9 | 0 | x | , | i | n | w | v | g | ' |
       -----------------------------------------

(The key with | and \ on it tends to live in different places on different keyboards. Wherever it is, in my experience it doesn't move for the Dvorak layout.)

The second layout is more common on modern computers, and other variants appear to exist.

August Dvorak and his brother-in-law William Dealey invented this "simplified" keyboard layout in the early 1930s. (The sources I looked up had 1932 and 1936 as dates, so I don't know which for sure.) Although August Dvorak is related to Antonín Dvořák, August's name is Americanized and is not pronounced with the Czech accented R. (It's a Dvorak keyboard, not a "dvorzhak"!)

The Dvorak keyboard was designed for efficiency and reduction of finger strain. The QWERTY keyboard was designed to prevent typewriter hammers from jamming.

Take note! Dvorak layout is not going to make you into some kind of typing whiz. It wasn't made for "speed" but for comfort. Speed may be an effect, and there are fast typists who use Dvorak, but I'm not sure if there are fair studies checking a correlation.

Windows has the Dvorak layout built in. Go to Start | Settings | Control Panel | Keyboard | Language | Properties | Keyboard Layout | United States-Dvorak.

Redhat Linux gave me the option to choose the Dvorak layout among other 'languages' at install. I would not know how to change this afterwards. The default Dvorak .Xmodmap for X used the ANSI layout instead of the usual one, which was confusing. (But now I know a bit more about .Xmodmap files...)

Multiple-mapped keyboards are available that can switch between Dvorak and QWERTY at the press of a button. The Apple IIc computer had this function built-in. (Ah, modern science!)

Major drawback of using Dvorak on computers: many programs, especially games, use key maps by location, rather than by meaning. For example, they might use I J K L for arrow keys. This makes things very difficult for non-QWERTY layouts. In addition, control-Z, control-X, control-C, and control-V (usually undo, cut, copy, and paste, respectively) no longer are next to each other (but I'll bet you never noticed they were in the first place).

The single-handed Dvorak layouts were invented in 1945 in response to the request of a Colonel Robert Allen, who lost an arm in World War II.

Dvorak was designed with the English language in mind. I don't know how 'efficient' it would be for other languages.

Some stats:

22% of keystrokes are on the Dvorak upper row.
56% are on the QWERTY upper row.

70% of keystrokes are on the Dvorak home row.
31% are on the QWERTY home row.

8% of keystrokes are on the Dvorak bottom row.
16% are on the QWERTY bottom row.

(Of course, the home row is the "ideal position" for your keystrokes to be.)

The 'logic' of the keyboard: It's good to not have to type long strings of letters with one hand: better to type a bit with one hand while you get your other hand in position for the next letters. Dvorak accomplishes this by putting all the vowels on the left hand. It also moves the more common letters to the home row, saving your fingers the excess mileage of running around everywhere.

I use the Dvorak layout on my computer, and it's really fun to see people freak out when they try to type things out on my computer and see all the keys are in the wrong places. (To add to the mayhem I also have my mouse buttons reversed.)

Anyway, Dvorak layout is nice, but I'm not going to evangelize to you about it. You can try it if you like, but be prepared to type a lot slower until your fingers get the hang of it. You get a lot of new finger motions in that you don't get in QWERTY--I remember my fingers felt pretty muscular the first few weeks. In any event it'd be a fun skill to show off anytime you come by to use my computer.