I'm new in Android development. I'm looking for any method that applies pitch shifting to output sound (in real-time). But I couldn't find any point to start.
I've found this topic but I still don't know how can I apply this.
Any suggestions?
In general, the algorithm is called a phase vocoder -- searching for that on the Internets should get you started.
There are a few open source phase vocoders out there, you should be able to use those for reference too.
You can do phase vocoder in real-time -- the main component used is the FFT, so you'll need a fast FFT. The Android libraries can do this for you, see this documentation: http://developer.android.com/reference/android/media/audiofx/Visualizer.html
As it happens, I'm about to release an open source FFT for ARM that is faster than Apple's vDSP library (which was hitherto the fastest). I'll post back in a few days when I've uploaded it to github.com.
Good luck.