Hi,
From your description, you want to fire javascript when the value of DateTime Picker changes.
We can override the OnPickerFinish function in DatePicker.js to fire the event when the date is updated from the date picker like this:
function OnPickerFinish(resultfield)
{
clickDatePicker(null,"","");
//your code here
alert(resultfield.value);
}
This link will show how to override the OnPickerFinish function:
http://theway4ward.wordpress.com/2013/07/30/211/
Before coding, a jQuery Library for SharePoint Web Services needs to be downloaded, then we can upload this jQuery Library to a SharePoint document library and reference it at the head of the script like this:
<script type="text/javascript" src="http://code.jquery.com/jquery-1.10.2.min.js"></script>
<script type="text/javascript" src="http://yoursite/yourdocumentlibrary/jquery.SPServices-2013.01.min.js"></script>
The jquery.SPServices-2013.01.min.js can be downloaded from:
http://spservices.codeplex.com/SourceControl/latest
Feel free to reply if you have any questions.
best regards