When it comes to adding penalty shots there are some options to choose from.
If you are taking a penalty drop (out of an unplayable lie or a hazard) you should use 'Drop Ball' option. You can apply this by clicking on the shot that resulted in you needing to take a drop (the shot that ended up in the hazard or bush etc). Then clicking the 'Drop Ball' option that appears.
A stroke penalty will be added as the second shot and you can move the red node to where the shot finished in the hazard etc. After this you can then move the location of the third shot to where you dropped the ball.
If you lost a ball and need to add a penalty shot you should do this by using the 'Lost Ball' option. You can apply this by clicking on the shot that resulted in lost ball. Then clicking the 'Lost Ball' option that appears.
This will add a penalty shot to your score and create a new third shot from the tee box. You can then place where the lost ball finished roughly and edit the newly created third shot if needed.
Penalty shots (rules infringement)
If you break the rules as you play and need to add penalty shots to your score you can apply this by clicking on the '+' sign on the map, click on either the 1 stroke or 2 stroke penalty, click on 'Add Shot' and then click on the map where this happened.