Retrieving sensor information from the onboard sensors:

public class MainActivity extends Activity implements SensorEventListener {
 
    private SensorManager mSensorManager;
    private Sensor accelerometer;
    private Sensor gyroscope;

    float[] accelerometerData = new float[3];
    float[] gyroscopeData = new float[3];
 
    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);
 
        mSensorManager = (SensorManager) getSystemService(SENSOR_SERVICE);
 
        accelerometer = mSensorManager.getDefaultSensor(Sensor.TYPE_ACCELEROMETER);
        gyroscope = mSensorManager.getDefaultSensor(Sensor.TYPE_GYROSCOPE);
 
    }
 
    @Override
    public void onResume() {
        //Register listeners for your sensors of interest
        mSensorManager.registerListener(this, accelerometer, SensorManager.SENSOR_DELAY_FASTEST);
        mSensorManager.registerListener(this, gyroscope, SensorManager.SENSOR_DELAY_FASTEST);
        super.onResume();
    }
 
    @Override
    protected void onPause() {
        //Unregister any previously registered listeners
        mSensorManager.unregisterListener(this);
        super.onPause();
    }
 
    @Override
    public void onSensorChanged(SensorEvent event) {
        //Check the type of sensor data being polled and store into corresponding float array
        if (event.sensor.getType() == Sensor.TYPE_ACCELEROMETER) {
            accelerometerData = event.values;
        } else if (event.sensor.getType() == Sensor.TYPE_GYROSCOPE) {
            gyroscopeData = event.values; 
        }
    }
 
    @Override
    public void onAccuracyChanged(Sensor sensor, int accuracy) {
        // TODO Auto-generated method stub
    }
}

The sensor values returned by Android are with respective to the phone's coordinate system (e.g. +Y points towards the top of the phone). We can transform these sensor values into a world coordinate system (e.g. +Y points towards magnetic North, tangential to the ground) using the sensor managers rotation matrix

First, you would need to declare and initialize the matrices/arrays where data will be stored (you can do this in the onCreate method, for example):

float[] accelerometerData = new float[3];
float[] accelerometerWorldData = new float[3];
float[] gravityData = new float[3];
float[] magneticData = new float[3];
float[] rotationMatrix = new float[9];

Next, we need to detect changes in sensor values, store them into the corresponding arrays (if we want to use them later/elsewhere), then calculate the rotation matrix and resulting transformation into world coordinates:

public void onSensorChanged(SensorEvent event) {
    sensor = event.sensor;
    int i = sensor.getType();

    if (i == Sensor.TYPE_ACCELEROMETER) {
        accelerometerData = event.values;
    } else if (i == Sensor.TYPE_GRAVITY) {
        gravityData = event.values;
    } else if (i == Sensor.TYPE_MAGNETIC) {
        magneticData = event.values;
    }

    //Calculate rotation matrix from gravity and magnetic sensor data
    SensorManager.getRotationMatrix(rotationMatrix, null, gravityData, magneticData);

    //World coordinate system transformation for acceleration
    accelerometerWorldData[0] = rotationMatrix[0] * accelerometerData[0] + rotationMatrix[1] * accelerometerData[1] + rotationMatrix[2] * accelerometerData[2];
    accelerometerWorldData[1] = rotationMatrix[3] * accelerometerData[0] + rotationMatrix[4] * accelerometerData[1] + rotationMatrix[5] * accelerometerData[2];
    accelerometerWorldData[2] = rotationMatrix[6] * accelerometerData[0] + rotationMatrix[7] * accelerometerData[1] + rotationMatrix[8] * accelerometerData[2];

}

Add the following code to the onCreate()/onResume() method:

SensorManager sensorManager;
Sensor mAccelerometer;
final float movementThreshold = 0.5f;  // You may have to change this value.
boolean isMoving = false;
float[] prevValues = {1.0f, 1.0f, 1.0f};
float[] currValues = new float[3];

sensorManager = (SensorManager)getSystemService(SENSOR_SERVICE);
mAccelerometer = sensorManager.getDefaultSensor(Sensor.TYPE_ACCELEROMETER);
sensorManager.registerListener(this, mAccelerometer, SensorManager.SENSOR_DELAY_NORMAL);

You may have to adjust the sensitivity by adapting the movementThreshold by trial and error. Then, override the onSensorChanged() method as follows:

@Override
public void onSensorChanged(SensorEvent event) {
    if (event.sensor == mAccelerometer) {
        System.arraycopy(event.values, 0, currValues, 0, event.values.length);
        if ((Math.abs(currValues[0] - prevValues[0]) > movementThreshold) ||
                (Math.abs(currValues[1] - prevValues[1]) > movementThreshold) ||
                (Math.abs(currValues[2] - prevValues[2]) > movementThreshold)) {
            isMoving = true;
        } else {
            isMoving = false;
        }
        System.arraycopy(currValues, 0, prevValues, 0, currValues.length);
    }       
}

If you want to prevent your app from being installed on devices that do not have an accelerometer, you have to add the following line to your manifest:

<uses-feature android:name="android.hardware.sensor.accelerometer" />