Our scenario is: FirstActivity call SecondActivity and when SecondActivity is finish his job we must pass some data to FirstActivity.
For this we are starting SecondActivity like that:

Intent i = new Intent(this, SecondActivity.class);
startActivityForResult(i, 901);

Before we "finish" SecondActivity we must set some data like

Intent returnIntent = new Intent();
returnIntent.putExtra("data",EXTRA_DATA_HERE);
setResult(RESULT_OK,returnIntent);
finish();

Or if we don't want to return data / just like if something is wrong

setResult(RESULT_CANCELED, new Intent());
finish();

And after that in our FirstActivity class we must write something like:

protected void onActivityResult(int requestCode, int resultCode, Intent data) {
    if (requestCode == 901) {
        if(resultCode == RESULT_OK){
            String result=data.getStringExtra("data");
        }
        if (resultCode == RESULT_CANCELED) { // we don't have data		
        }
    }
}

More information about Activities in Android can be found at Android developer documentation.