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).

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.

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.

R Rectangle 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.

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
  "flow", which is the number of
  pixels scattered with each click.

M Mark tool. Marks a rectangular
  area of the tile to use with the
  clone tool.

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.

Backspace flips the tile horizontally.

CTRL+Backspace flips the tile
  vertically.

[ Rotates the tile 90 degrees
  counterclockwise.

] Rotates the tile 90 degrees
  clockwise.