Xaml bind object to each cell of a datagrid

am new to wpf and C# and mvvm. Currently am working on a Reversi game ,specificaly ui and viewmodel.

In the Vm I currently have setup this hierarchy --> the Vm contains a List of RowVieModels ---> the RowViewModels have a list of SquareViewModels --> each SquareViewModel represent a square on the reversi gameboard.

the thing am stuck on is how can I bind each SquareViewModel to the grid on my xaml ui? The thing I've thought up is to bind each RowViewModel to a row on the grid and from there bind each square but I don't know how to do the binding.

this is the SquareViewModel

 class SquareViewModel
{
    private ICell<ISquare> square;

    public ISquare squareproperty
    {


        get { return this.square.Value; }
        private set { this.square.Value = value; }
    }


    public SquareViewModel(ISquare square)
    {
        this.square.Value = square;



    }


    public Player getOwner()
    {

        return this.square.Value.Owner.Value;

    }
    public void zetSteen(Player player)
    {
        this.square.Value.Owner.Value = player;



    }

    public bool isValidMove()
    {


        return this.square.Value.IsValidMove.Value;

    }

    public Vector2D getPositie()
    {


        return this.square.Value.Position;

    }

}
}

and this is the grid I want to bind to

            <DataGrid  x:Name="grid"  Background="AntiqueWhite" Width="400px" Height="400px"  >

Thanks in advance!