Just for an example, let’s say that you have a button on a form that just want to popup an alert that says “HEY” when it is clicked.

protected void btnHey_Click(object sender, EventArgs e)
{
     StringBuilder sb = new StringBuilder();
     sb.Append("<script language='javascript'>alert('HEY');</script>");

     // if the script is not already registered
     if (!Page.ClientScript.IsClientScriptBlockRegistered(Page.GetType(), "HeyPopup"))
          ClientScript.RegisterClientScriptBlock(Page.GetType(), "HeyPopup", sb.ToString());
}

To run a method that is already defined in the .aspx page, you would use similar code, but with one difference:

// javascript method
<script language="javascript" type="text/javascript">
    function ShowMessage(myMessage){
        alert(myMessage);
    }
</script>

// C# code
protected void btnHey_Click(object sender, EventArgs e)
{
   StringBuilder sb = new StringBuilder();
   sb.Append("ShowMessage('hey');");

   // if the script is not already registered
   if (!Page.ClientScript.IsClientScriptBlockRegistered(Page.GetType(), "HeyPopup"))
       // notice that I added the boolean value as the last parameter
       ClientScript.RegisterClientScriptBlock(Page.GetType(), "HeyPopup", sb.ToString(), true);

And it’s that simple.