This can be achieved in different ways.
1. Using javascript (purely client side)
2. Using AJAX
Take a look at the MSDN article on
Working with Client-side Script[
^]. Since you are new to asp.net, its worth spending sometime.
Coming to your question, set the onchange attribute in codebehind page as
ddl.Attributes["onchange"] = "javaScriptFunctoChangeTextbox();";
And you add the javascript in the aspx page.