Select a cell by mousing over it or use the arrow keys to move the active cell.
Place a number in the active cell with the number keys.
Press delete to remove the cell contents.
Press shift to activate "notes" mode.  Shift+number to place a note for the number in the active cell.
Press the "f" key when the active cell contains a label to see factors for that group/house. E.g.  if the active cell shows "84x", f will show you all possible factors for 84.
Press the "z" key to undo your move; "y" key to redo a move

Hint button reveals a random empty cell's answer.
Solve button finishes the puzzle.
Fill Notes will add an initial set of notes for a sudoku puzzle.  Not very smart.
Check Moves will validate all cells.
Show Highlights will toggle highlighted cells in sudoku games
Clone board will copy the current state of the board so you can try out guesses and then Dismiss a contradictory board to resume from the point of cloning.
New Game will start a new game with the given game ID, difficulty and/or size (depending on the game type)