How to populate c# windows forms combobox?

Below are the important properties for you.

ComboBox.DataSource Property

A data source can be a database, a Web service, or an object that can
later be used to generate data-bound controls. When the DataSource
property is set, the items collection cannot be modified.

ComboBox.DisplayMember Property

A String specifying the name of an object property that is contained
in the collection specified by the DataSource property. The default is
an empty string (“”).

ComboBox.ValueMember Property

A String representing the name of an object property that is contained
in the collection specified by the DataSource property. The default is
an empty string (“”).

DataTable dataTable = GetDataTable("Select * from Student"); // You have to implement the ways to retrieve data from the database.
comboBox1.Datasource = dataTable;
comboBox1.DisplayMember = StudentName; // Column Name
comboBox1.ValueMember = StuentId;  // Column Name

Here is one way if you want to add items programmatically.

private class Item 
{
      public string _Name;
      public int _Id

      public Item(string name, int id) 
      {
          _Name = name; 
          _Id = id;
      }

      public string Name
      {
          get { return _Name; }
          set { _Name = value; }
      }

      public string Id
      {
          get { return _Id; }
          set { _Id = value; }
      }
}   

comboBox1.DisplayMember = "Name";
comboBox1.ValueMember = "Id";

comboBox1.Items.Add(new Item("Student 1", 1));
comboBox1.Items.Add(new Item("Student 2", 2));
comboBox1.Items.Add(new Item("Student 3", 3));

There are various ways of doing this.

How to: Add and Remove Items from a Windows Forms ComboBox

ComboBox.Items Property