C#
BasicsEntities m_context = new BasicsEntities();
..
IQueryable<person> personsQuery = m_context.CreateObjectSet<person>();
string lastName = personsQuery.First().lastName;

C#
IQueryable<person> personsWithDepartmentsQuery = m_context.CreateObjectSet<person>().Include("department");
string deptName = personsWithDepartmentsQuery.First().department.name;

C#
IQueryable query = from p in m_context.persons
                   select p;

C#
using System.Data.Objects;  // System.Data.Entity.dll
...
IQueryable query = from p in m_context.persons select p;

listBox1.DisplayMember = "LastName";
listBox1.DataSource = ((ObjectQuery) query).Execute(MergeOption.AppendOnly);

C#
person person1 = new person { firstName = "Zbynek", lastName = "Cernin", department_id = 1 };
m_context.persons.AddObject(person1);
m_context.SaveChanges();

C#
m_context.persons.DeleteObject(m_context.persons.Last());
m_context.SaveChanges();

C#
// load data
IQueryable query = from pers in m_context.persons
                   select pers;

dataGridView1.DataSource = ((ObjectQuery)query).Execute(MergeOption.AppendOnly);
// or based on you data model
// dataGridView1.DataSource = ((System.Data.Entity.Infrastructure.DbQuery<Person>>)query).ToList();  

//Save changes after edit
dataGridView1.EndEdit();
m_context.SaveChanges();

C#
// EF 6
// code for a button event handler

// delete rows in database
foreach (var row in dataGridView1.SelectedRows)
{
    object o = ((DataGridViewRow)row).Cells[ID_INDEX].Value;
    int id = Convert.ToInt32(o); // (int)o throws InvalidCastException
    _dbContext.Persons.Remove(_dbContext.ElementExtern.Where(el => el.Id == id).First());
}
_dbContext.SaveChanges();

// delete rows in Grid
for (int i = dataGridView1.Rows.Count - 1; i >= 0; i--)
{
    if (dataGridView1.Rows[i].Selected)
    {
        dataGridView1.Rows.RemoveAt(i);  // dataGridView1.DataSource must be bound to BindingSource in order to allow RemoveAt() to run
    }
}

In order to achieve this you need to create a helper class that will hold references to original entities loaded by entity framework and properties for the columns that will be shown in the DataGridView

C#
    public class QueryData
    {
        public Person Person;
        public Department Department;

        public long Id
        {
            get { return Person.Id; }
        }

        public string Name
        {
            get { return Person.Name; }
            set { Person.Name = value; }
        }

        public string DepartmentName
        {
            get { return Department.Name; }
            set { Department.Name = value; }
        }
    }

Then it is possible to read data and display it in the DataGridView

C#
  var query = from p in _dbContext.Persons
                 join d in _dbContext.Department on p.DepartmentId equals d.Id into d1
                 from d2 in d1.DefaultIfEmpty()
                 select new QueryData { Person = p, Department = d2 };
  
  BindingSource bs = new BindingSource(); // without BindingSource it is not possible to call: dataGridView1.Rows.RemoveAt(i);
  bs.DataSource = query.ToList();
  
  dataGridView1.DataSource = bs;
  dataGridView1.Refresh();
}

You need a class that represents internal data (e.g. value in DB) and text presented to the user

C#
public class Gender
{
    public int Code { get; set;}
    public string Name { get; set; }
}

Create list manually or read it from DB (e.g .from a table)

C#
List>Gender< genders = new List>Gender<();
genders.Add(new ElementType() { TypeCode = "0", Name = "Female" });
genders.Add(new ElementType() { TypeCode = "1", Name = "Male" });

Create combo box column type

C#
DataGridViewComboBoxColumn columnType = new DataGridViewComboBoxColumn();
columnType.DataPropertyName = "Gender";  // name of the public property in the class that is datasource for the DataGridView (QueryData in the example above) 
columnType.DataSource = genders;
columnType.ValueMember = "TypeCode";
columnType.DisplayMember = "Name";

Assign it to the DataGridView

C#
dataGridView1.Columns.Insert(2, columnType);