This way
<asp:TextBox ID="txtFruit" runat="server" />
<asp:Button ID="btnAdd" runat="server" Text="Add Item" OnClick="AddItem" />
<br />
<asp:DropDownList ID="ddlFruits" runat="server">
<asp:ListItem Text="----Fruits----" Value=""></asp:ListItem>
</asp:DropDownList>
protected void AddItem(object sender, EventArgs e)
{
string fruit = txtFruit.Text.Trim();
if (!string.IsNullOrEmpty(fruit))
{
ddlFruits.Items.Add(new ListItem(fruit, fruit));
}
}