[Serializable]
    public class Person
    {
        public string name { get; set; }
        public string surename { get; set; }
        public string birthday { get; set; }
        public string sex { get; set; }
        public string country { get; set; }
        public string city { get; set; }
        public int growth { get; set; }
        public int weight { get; set; }
        public string hair_color { get; set; }
        public string eye_color { get; set; }
        public string zodiac_sign { get; set; }

        public Person()
        {
            name = null;
            surename = null;
            birthday = null;
            sex = null;
            country = null;
            city = null;
            growth = 0;
            weight = 0;
            hair_color = null;
            eye_color = null;
            zodiac_sign = null;
        }
    }

private void btSave_Click(object sender, EventArgs e)
        {
            Person[] persons = new Person[dataGridView1.RowCount];
            for(int i = 0; i < dataGridView1.RowCount; i++)
            {
                persons[i] = new Person();
                //Дальше загвоздка...
            }
        }