Usage:
Select the opponent you're playing against at the top.
("Perfect opponent" is a hypothetical ideal opponent who only plays perfectly, and assumes you will do the same. They are not in the game.)
Draw the board you want to get a solution for by clicking/tapping on the spaces.
You can also use the mouse wheel to quickly select dice.
Right click / long tap a die to clear it (and shift any dice above/below it).
On the bottom left, choose the die you rolled (which you need to place next).
You will see the best move (or moves, if they're equivalent) highlighted in green.
Your chances of winning (assuming perfect play) are displayed below. You can tap on the results to "accept" the move and apply it to the board.
If you see any red squares while drawing the board, these are errors. Fix them, or hover over the error to see what the problem is.
Click ↻ to reset the board to a new game. You can use your web browser back and forward buttons to undo / redo.
The solver always assumes that it's your (the bottom player's) turn. The ⇕ button flips the board around, if you want to examine your opponent's options.
Note that some answers may seem counter-intuitive at first glance. They are correct anyway.
Links: