DataTable dt = new DataTable();
dt.Columns.Add("first_col", typeof(String));
dt.Columns.Add("second_col", typeof(String));

BindingSource bs = new BindingSource();
bs.DataSource = dt;
DataGridView dgv = new DataGridView();
dgv.DataSource = bs;
dgv.Dock = DockStyle.Fill;
dgv.ScrollBars = ScrollBars.Both;

Button btn1 = new Button();
btn1.Left =  5 ;
btn1.Top =  50 ;
btn1.Text = "Press Me!";
btn1.Click += delegate(object snd, EventArgs ea)
    {
        for (int i =  0 ; i <  1000 ; i++)
        {
            DataRow r = dt.NewRow();
            r[ 0 ] = i.ToString();
            r[ 1 ] = (i *  2 ).ToString();

            dt.Rows.Add(r);
        }
    };

TextBox txt = new TextBox();
txt.Text = "";
txt.Width =  200 ;
txt.Left =  300 ;
txt.Top =  50 ;
txt.DataBindings.Add(new Binding("Text", bs, "first_col"));

this.Controls.AddRange(new Control[] { btn1, txt, dgv });