Here are the steps I went through in getting ffmpeg to work on Android:
1. Build static libraries of ffmpeg for Android. This was achieved by building olvaffe's ffmpeg android port (libffmpeg) using the Android Build System. Simply place the sources under /external and make away. You'll need to extract bionic(libc) and zlib(libz) from the Android build as well, as ffmpeg libraries depend on them.
2.Create a dynamic library wrapping ffmpeg functionality using the Android NDK. There's a lot of documentation out there on how to work with the NDK. Basically you'll need to write some C/C++ code to export the functionality you need out of ffmpeg into a library java can interact with through JNI. The NDK allows you to easily link against the static libraries you've generated in step 1, just add a line similar to this to Android.mk: LOCAL_STATIC_LIBRARIES := libavcodec libavformat libavutil libc libz
3. Use the ffmpeg-wrapping dynamic library from your java sources. There's enough documentation on JNI out there, you should be fine.
Regarding using ffmpeg for playback, there are many examples (the ffmpeg binary itself is a good example), here's a basic tutorial. The best documentation can be found in the headers.