/* DataTable #1 */
DataTable dt1 = new DataTable();
dt1.Columns.Add(new DataColumn("author", typeof(string)));
dt1.Columns.Add(new DataColumn("name", typeof(string)));
dt1.Columns.Add(new DataColumn("date", typeof(DateTime)));
dt1.Columns.Add(new DataColumn("id", typeof(int)));
dt1.Columns.Add(new DataColumn("check", typeof(bool)));

BindingSource bs1 = new BindingSource();
bs1.DataSource = dt1;

DataGridView dgv1 = new DataGridView();
dgv1.DataSource = bs1;
dgv1.Dock = DockStyle.Fill;

for (int i =  0 ; i <  10 ; i++)
{
    DataRow row = dt1.NewRow();
    row[ 0 ] = string.Format("Author {0}", i.ToString());
    row[ 1 ] = string.Format("Name {0}", i.ToString());
    row[ 2 ] = DateTime.Now;
    row[ 3 ] = i;
    row[ 4 ] = (bool)(i %  2  ==  1 );

    dt1.Rows.Add(row);
}

/* DataTable #2 */
DataTable dt2 = new DataTable();
dt2.Columns.Add(new DataColumn("author", typeof(string)));
dt2.Columns.Add(new DataColumn("name", typeof(string)));
dt2.Columns.Add(new DataColumn("date", typeof(DateTime)));
dt2.Columns.Add(new DataColumn("id", typeof(int)));
dt2.Columns.Add(new DataColumn("check", typeof(bool)));

BindingSource bs2 = new BindingSource();
bs2.DataSource = dt2;

DataGridView dgv2 = new DataGridView();
dgv2.DataSource = bs2;
dgv2.Dock = DockStyle.Fill;

/* DataSet */
DataSet ds = new DataSet();
ds.Tables.AddRange(new DataTable[] { dt1, dt2 });

/* Other visual */
Button btn = new Button();
btn.Text = "Press Me!";
btn.Left =  10 ;
btn.Top =  10 ;
btn.Width =  150 ;
btn.Click += delegate
{
    /* ищем всё, что помечено галочками */
    foreach (DataRow r in dt1.Rows)
    {
        if ((bool)r["check"] == true)
        {
            dt2.ImportRow(r);
        }
    }
};

SplitContainer sub_sc = new SplitContainer();
sub_sc.Orientation = Orientation.Horizontal;
sub_sc.Dock = DockStyle.Fill;
sub_sc.Panel1.Controls.Add(dgv1);
sub_sc.Panel2.Controls.Add(btn);

SplitContainer sc = new SplitContainer();
sc.Dock = DockStyle.Fill;
sc.Panel1.Controls.Add(sub_sc);
sc.Panel2.Controls.Add(dgv2);

Controls.AddRange(new Control[] { sc });