You can use arrow keys or the mouse.

Left-Click on pixels to draw (or press SPACE).
Right-Click to select the color under the cursor (or press ENTER or G (Grab)).

Left click on a color in the palette at the bottom to select it. (ALT + arrow keys will pick palette colors too!)

See the "Undo" bar along the right? Click there to revert to an earlier state, or press CTRL+Z to go back one step, so to speak.

Hold SHIFT to move faster with the arrow keys. Press SHIFT+S to slow down the SHIFT-move speed and SHIFT+F to make it faster.

On the left is a panel of tool buttons. Each of them can also be triggered with a keypress.

D Draw tool. Use this for single
  pixels or free-hand lines.

B Box tool. Use this to draw
  filled rectangles.

L Line tool. Use this to draw
  straight lines.

F Fill tool. Use this to flood-fill
  paint an area. Like the paint
  bucket in Photoshop.

R Replace tool. Use this to replace
  one colour with another.

O Circle tool. Use this to draw non-
  filled circles. The first click
  defines the center of the circle.

A Airbrush tool. Use this to scatter
  pixels around. While the airbrush
  is active, you can press + and -
  to change the scatter area, and
  CTRL+ and CTRL- to change the
  "mist", which is the number of
  pixels scattered with each click.

S Scroll tool. While this is the
  selected tool, you can click and
  drag on the tile, or press arrow
  keys, to move it around. Pixels
  will wrap over the edges.

M Mark tool (Copy). Marks (copies) a
  rectangular area of the tile to
  use with the clone tool.

  Mark, alternate tool (Cut):
  Right Click or hold CTRL or SHIFT
  while clicking or pressing SPACE
  to cut a piece from the sprite
  instead of copying it. Great for
  moving parts of the tile!

C Clone tool. Draw on the tile using
  a portion of a tile that you have
  previously chosen with the Mark
  tool. Pixels drawn in color 0
  (normally black) will be
  transparent. While you are using
  the clone tool, you can hold the
  ENTER key or the right mouse button
  and move the center of the cloned
  area

Backspace flips the tile horizontally.

CTRL+Backspace flips the tile
  vertically.

[ Rotates the tile 90 degrees
  counterclockwise.

] Rotates the tile 90 degrees
  clockwise.

P or left mouse button on preview
  Switch preview area at the bottom 
  left between neighbouring tiles and
  single tile preview. 

Press `/~ (backtick/tilde) to toggle whether the cursor displays normally or as a single pixel.

CTRL+S saves the tile immediately without exiting, which is useful if you are live-previewing the game.
