It might sound straight forward but as it happens it's anything but...
On iOS and Android I simply hand the "picture taking" part off to the default app so I don't have to create something myself from scratch (taking pictures isn't that important in my app).
Windows phone 8.1 seems to be missing all that basic functionality and also seems to expect the dev to build everything from scratch.
You used to have CameraTask and PhotoChooser for just that but it only works for wp 7 and 8, not 8.1.
Then there's the CameraCaptureUI which does something similar but is, once more, not available for freaking wp 8.1.
I have tried the media.capture API but that kept throwing "wrong function" exceptions and seems to expect that you place some preview element inside the xaml if you wish to actually see what you are recording.
The issue with that is that i don't really want (I don't even think it's possible) to create a page just so i can take a picture on windows phone.
How then should I go about taking a simple fucking picture on windows phone 8.1, saving it and then displaying it? It's no wonder nobody likes to develop for windows phone, it sucks balls... 9/10 if something breaks it breaks on windows phone and it only breaks on windows phone.
ps: that makes 3 fucking different ways for accessing the camera, neither of which can be used on all versions, for what is essentially one operating system... Way to go microsoft.