pseduocode
aspx code
//Asume one button control id="bttnAjax" and one textbox in content template of update pannel id=txtAjax"
<asp:UpdatePanel ID="UpdatePanel1" runat="server" >
<Triggers >
<asp:AsyncPostBackTrigger ControlID="bttnAjax" EventName="click"/>
</Triggers>
<ContentTemplate>
<asp:TextBox ID="txtAjax" runat ="server"/>
</ContentTemplate>
</asp:UpdatePanel>
Code Behind
protected void bttnAjax_Click(object sender, EventArgs e)
{
txtAjax.Text="Welcome To Ajax World "
}