I edited an existing validated function (included in a WordPress plugin) to add email validation feature.
function validateForm(form){
    var $ = jQuery;
// The code snippet I added
// **********************************
var emailID = document.getElementsByName('useremail')[0].value;
    atpos = emailID.indexOf("@");
    dotpos = emailID.lastIndexOf(".");
   if (atpos < 1 || ( dotpos - atpos < 2 ))
    {
        alert("Please enter correct email ID")
        return false;
    }
// End of the code added by me
else if(!$('input[name=title]', form).val()){
     alert("Please enter correct Name")
    $('input[name=title]', form).focus();
    return false;
    }
// ...
return true;
}
The html code:
<input type="text" name="useremail" id="useremail" required>
The email validation code was derived from Validate email address in JavaScript?.
I think the part var emailID = document.getElementsByName('useremail')[0].value; is not correct. 
I tried also to use var emailID = document.getElementById('useremail'); which also does not work. 
Added: var emailID = document.getElementById('useremail'); should work. The problem was that the js file was not properly enqueued in WordPress. Thanks for all comments.
 
     
    