Best How To :

Firstly to address why no data is being loaded. In your Update() method you first initialize a new instance of ManageUser, whose default value for Username will be null (the default for typeof string). You then call user.GetData(user.Username); which passes null to the method and based on

if (string.IsNullOrEmpty(Username)) // it is!
{
  cmd.Parameters["@Username"].Value = DBNull.Value;
}

your query then returns all Users whose Username field is null. If you database does not contain any rows where Username IS NULL no rows are returned, therefor there is no data to display.

However including this method in your model is bad practice (and what about other methods such as fetching all users?). Start by adding the following 2 classes to your Data folder

public interface IUserDB
{
  List<User> Fetch();
  User Get(int ID);
}
public class UserDB : IUserDB
{
  public List<User> Fetch()
  {
    List<User> users = new List<User>();
    using (SqlConnection conn = new SqlConnection(connectionString))
    {
      string query = "SELECT [Username], [EmployeeID] FROM [User];
      conn.Open();
      using (SqlCommand cmd = new SqlCommand(query, conn))
      {
        using (SqlDataReader reader = cmd.ExecuteReader())
        {
          while (reader.Read())
          {
            User user = new User();
            user.Username = reader["Username"].ToString();
            user.ID = reader["EmployeeID"].ToString();
            users.Add(user);
          }
        }
      }
    }
    return users;
  }
  public User Get(int ID)
  {
    User user = new User();
    using (SqlConnection conn = new SqlConnection(connectionString))
    {
      string query = "SELECT [Username], [EmployeeID] FROM [User] WHERE [EmployeeID] = @ID";
      conn.Open();
      using (SqlCommand cmd = new SqlCommand(query, conn))
      {
        cmd.Parameters.Add("@EmployeeID", SqlDbType.Int).Value = ID;
        using (SqlDataReader reader = cmd.ExecuteReader())
        {
          if (!reader.Read())
          {
            return null;
          }
          user.ID = reader["EmployeeID"].ToString();
          user.UserName = reader["Username"].ToString();  
        }
      }
    }
    return user;
  }
}

Side notes: You do not need to call Dispose() - the using statement takes care of that. The purpose of the interface may not be obvious yet, but once you gain some experience and understand Dependency Injection it will be. Its not clear why a table named User would have a field named EmployeeID - it should be UserID or better, just ID. There is no need to call if (reader.HasRows).

Then change your class to

public class User
{
  [Required(ErrorMessage = "Please fill-in Username.")]
  [Display(Name = "Username:")]
  public string UserName { get; set; }

  [Required(ErrorMessage = "Please fill-in Employee ID.")]
  [Display(Name = "ID:")]
  public string ID { get; set; }
}

Notes: A class name should reflect what it is, not what is does - it should not contain verbs such as "Manage".

Now in the controller, you can can call these methods to construct your views

public Controller UserController : Controller
{
  UserDB _Repository = new UserDB(); // later you will use DI
  public ActionResult Index()
  {
    List<User> model = _Repository.Fetch();
    return View(model);
  }
  public ActionResult Edit(int ID)
  {
    User model = _Repository.Get(ID);
    if (model == null)
    {
      return new HttpNotFoundResult();
    }
    return View(model);
  }
}

Your Index.cshtml view might then look like

@model List<yourAssembly.User>
@foreach(var user in Model)
{
  @Html.ActionLink(user.UserName, "Edit", "User", new { id = user.ID }, null)
}

Clicking a a link will pass the users ID value to the Edit(int ID) method which in turn will return the User with that ID value.

Note also you Edit.cshtml view needs to include controls for editing, i.e @Html.TextBoxFor(m => m.UserName), not @Html.DisplayFor(m => m.UserName)