This i'ble will help you control an LED with an app over bluetooth from your smartphone.
Step 1: Things You'll Need...
An Arduino board.(An UNO would do, mine is a clone :p)
A bluetooth module (HC05 or HC06).
Step 2: Hook Things Up...
Connect the LED to the 13th pin of the Arduino and ground.
Connect the Tx of the module to the Rx of the Arduino and the Rx of the module to the Tx of the Arduino.
Connect the 5v pin of the modue to the 5v of the Arduino and the ground of the module to the ground of the Arduino.
Step 3: Coding...
Upload the given sketch bluetoothlights.ino to your board.
Remember to remove the Tx and Rx pins before uploading.
Step 4: The App...
Download the apk and install it.
Make sure bluetooth is turned ON on your phone and that the bluetooth module is already paired with your device.
If it asks for a passkey it's 1234.
Step 5: Great! Finished.
Now you're good to go.
Open the app, connect your module, and enjoy!