By the Loop through those elements to check which is checked. You can try document.getElementsByName(<button_name>) or document.getElementsByTagName("input") to get an array of input elements.
You can see this example of how to fetch the value of the checked button from a set of radio buttons with the name "selected".
You can do similar for check box.
<html>
<head>
<script type="text/javascript">
function get_radio_value() {
var inputs = document.getElementsByName("selected");
for (var i = 0; i < inputs.length; i++) {
if (inputs[i].checked) {
return inputs[i].value;
}
}
}
function onSubmit() {
var id = get_radio_value();
alert("selected input is: " + id);
}
</script>
</head>
<body>
<form onsubmit="onSubmit();">
<input name="selected" value="1" type="radio"/>1<br/>
<input name="selected" value="2" type="radio"/>2<br/>
<input name="selected" value="3" type="radio"/>3<br/>
<input type="submit" value="submit"/>
</form>
</body>
</html>