If you have only one group of radio button in page then use the following code
$$('input[type=radio]:checked').pluck('value');
If you have more than one group of radio button then use following code
$$('input:checked[type="radio"][name="my_radio_group"]').pluck('value');
$$ will get the element input (html tag) which is checked and whose type is radio with name my_radio_group and pluck the value attribute.
It will help you a lot.