List<MeineKlasse> list = new List<MeineKlasse>();
foreach (DataGridViewRow row in DataGridView1.Rows)
{
    MeineKlasse obj = new MeineKlasse();
    obj.id = (int)row.Cells["Id"].Value; 
    obj.Name = (string)row.Cells["Name"].Value;
    ...
    list.Add(obj);
}

private BindingList<Positionen> blPositionen;

void SpaltenAnzeigen()
{
    
    blPositionen = new BindingList<Positionen>();      
    dataGridView1.DataSource = blPositionen;
}

void DatenUebernehmen
{
    blPositionen.Add(new Positionen()
            {
                ArtikelNummer = comboBox1.Text
            }); 
 }

  void posIndexUp(DataGridView dg)
        {
            if (dg.SelectedCells.Count > 0)
            {
                int idx = dg.SelectedCells[0].OwningRow.Index;

                if (idx > 0)
                {
                    int col = dg.SelectedCells[0].OwningColumn.Index;

                    DataGridViewRowCollection rows = dg.Rows;
                    DataGridViewRow row = rows[idx];

                    rows.Remove(row);
                    rows.Insert(idx - 1, row);

                    dg.ClearSelection();
                    dg.Rows[idx - 1].Cells[col].Selected = true;
                }
            }
        }