In magento some times we need to validate some fields like username on its availability.
So in that case we need to run the validation function on an event change of the element
In order to do that we need to add an function for example onblur to the element as shown below

<input class="input-text required-entry" id="firstname" type="text" name="firstname" onblur="validate_field(this)"/>

and add the javascript function inside the script tag like below

function validate_field(id){
  Validation.validate(id);
}

Hope this post helps to add form validation on change in magento