Firstly, you may have already know you can make cell, row or column of
DataGridView select-able. In your case, make sure the DataGridView's
SelectionMode is set to RowHeaderSelect, or FullRowSelect.

Then, you can handle SelectionChanged event:

private void DataGridView1_SelectionChanged(...)
{
   if (DataGridView1.SelectedRows.Count==0) return;

   //Do something with the SelectedRows, it could be one row, or multiple
rows. For example:

   Label1.Text=DataGridView1.SelectedRows[0].Cells[0].Value.ToString();
   ...
}