You can do this by adding code on button click in
yourpage.aspx.cs
here is a sample code
protected void BtnSerch_Click(object sender, EventArgs e)
{
DataSet Ds = new DataSet();
SqlDataAdapter Da = new SqlDataAdapter();
SqlConnection Con;
if (DropDownList1.SelectedIndex !=0)
{
Con = new SqlConnection(" your Connextion String");
Con.Open();
Da = new SqlDataAdapter(" select * from yourtable where ColumnName = '"+DropDownList1.SelectedItem.Text+"' ",Com);
Da.Fill(Ds);
GridView1.DataSource=Ds;
GridView1.DataBind();
Con.Close();
}
}