On the PCB there is a hole next to the crown, stick a needle into the hole and push gently, at this moment the crown should come loose and you can pull it out.
Next, you can take out the module and remove the front buttons by removing the tiny ¾ rings that are around the buttons ( don't know how they are called ) Push the to the side with a small screwdriver. Be careful not to lose these, these are spring loaded and can "jump" away. Next take out the buttons and clean them and refurbish the case.
Be careful not to make the inside of the case wet, because water can get under the "dial" making stains on it. It's better to remove the crystal if you are going to polish/brush it.