Entity Framework adding record into many to many mapping table

Flying somewhat blind because you omitted what attributesentity has. However, you need to have a property for the connection to.CustomerGroups . Simply include the organizations you want to be associated to in that property. For instance, this would associate the entity with the group "foo bar" and give the group a new name.

using (var context = DataObjectFactory.CreateContext())
{
    entity.CustomerGroups = new List<CustomerGroup> { GroupName = "Foo bar" };
    context.Customers.Add(entity);
    context.SaveChanges();
    return entity.Id;
}

EF will automatically put a record into the relationship if it is set up properly.CustomerGroups likewise add a relationship to theCustomerInGroups table.

EDIT:

Attempting to add an already existentCustomerGroup to a fresh client. You should purchase theCustomerGroup you should add it to the Customer object you are inserting after removing it from the database.

using (var context = DataObjectFactory.CreateContext())
{
    var customerGroups = context.CustomerGroups.Where(...).ToList(); // get your CustomerGroup object(s) here, and ensure it's enumerated with ToList()
    entity.CustomerGroups = customerGroups;
    context.Customers.Add(entity);
    context.SaveChanges();
    return entity.Id;
}