The above as captured by the app is shown below with UI controls annotated.  
To measure the moon's altitude above the horizon, first pan and zoom (drag and pinch gestures) to bring the moon inside the circular cursor. The slider top left controls the cursor diameter. Hit auto-align to center, or use the nudge controls to center manually. Then hit pin to fix the measurement cord origin. 

Now hit the button top left (⟂) to  toggle a horizon cursor for matching against the visible horizon of the photo. We don't have an open sea horizon in this example, but the shoreline will do fine as a so-called 'horizon short'. You can again use  auto-align or the nudge controls to refine the match.

That's it for the altitude measurement. To do the sight reduction calculation and and plot the resulting line of position, hit the sextant icon button bottom left to export the measured altitude to Celestial Navigation 360. The latter opens directly in a New Sight wizard for the date/time and altitude it has received.

Don't forget to set Dip consistently with the horizon/short as you step through the wizard

Calibration check

The Angular Distance app's internal camera calibration relies on manufacturer specs which on some devices may be incomplete or inaccurate. So it's advisable to check it, as is easily done by shooting a moon/planet sight from known position determined via GPS or otherwise: When you set Assumed Position to match your actual position, the sights reduction  intercept becomes purely a measurement error. If the auto-calibration is healthy, this error shouldn't normally exceed 20 NM or so.

Bright stars at nautical twilight

As mentioned above, typical device cameras do not capture stars very well in general. Nevertheless , the very brightest  (Sirius, Vega, Arcturus..) often capture reasonably well at intermediate altitudes against the nautical twilight horizon.

Bubble horizon

On devices with a gravity sensor, the app annotates the capture image with  an artificial  ('bubble') horizon, dashed line of the screenshot above.  To snap to the bubble horizon, move the horizon cursor outside the image bounds and hit auto-align.
The accuracy of the bubble horizon varies somewhat between devices and conditions.