microcontroller bluetooth
In my experience getting Bluetooth running on Android is far easier than on iOS, as iOS does not support the Bluetooth Serial Port Protocol (SPP). Many places online sell Bluetooth modules that handle all the Bluetooth stack stuff internally - all you need to do is connect a microcontroller via UART, pair the module to your phone, and read/write to the socket in your Android app. The module handles all the Bluetooth stack stuff.

Some of the modules I've used are the Bluetooth Mate Silver (good documentation) and a generic Bluetooth module (cheap)

Also see this answer.