When you remove the battery you will see a small pink dot in the lower right corner. This is not the real water damage indicator. The real water damage paper, with the pink crosses, is inside the back cover.
Remove all the 8 screws on the back part using your Philips screwdriver. Make sure you choose the correct screwdriver for the screw size to prevent shaving the top of the screws. Next we need to remove this back cover to see the real water damage indicator. Put the screws into the plastic back cover you removed at the beginning to stop them rolling around.
The tricky part is removing this back cover. You can use a finger nail or a guitar pick. I used my fingernail first, then an old sim card like I mentioned above. You need to get the pick between the front face plate and metal. Put the old sim card in, then slowly move it around all the phone. You will hear clicks as you go, these clicks are the white clips coming free and releasing the back. Be gentle and move slowly, there is no rush.
Once you have removed all the back cover turn it over. The water indicator is a piece of white paper with purple X marks. The water indicator is located near the camera lens hole on the back cover. The square is about 0.7mm in width and height. The indicator paper is NOT on the electronics part! It’s on the underside of the plastic part you removed.
That’s all! There are other hidden water indicators around the internal components of the phone, but this big indicator on the back case is the main marking they use.
Here is a video of a Youtube user totally tearing down his new Samsung Galaxy S4 in a teardown video. This is what I used to learn the process before doing it on my phone. He is showing the moisture level sensor on the Samsung Galaxy S4 at 4.20 in the youtube video.