Create your button and your textbox controls:
<asp:textbox id="TheDateTB" runat="server" xmlns:asp="#unknown"></asp:textbox>
<asp:button id="TheButton" runat="server" text="Press me" onclick="TheButton_Click" xmlns:asp="#unknown" />
Then on Click event, set the date in the textbox:
protected void TheButton_Click(object sender, EventArgs e)
{
TheDateTB.Text = DateTime.Now.ToString("MM/dd/yyyy");
}