Applying MVVM pattern in a WPF application

If I'm understanding your question....

I think the approach you could take is by using DataTemplates, ItemsControl and perhaps ContentPresentor.

In effect what you want to do is tell WPF to "display" your view models. Because your view models are just plain classes, WPF does not know how to "render" them. This is where DataTemplates come in. The bonus of this approach is that the DataContext for the DataTemplate content will automatically be set to the view model. DataTemplates are defined in your Window or UserControl resources:

<Window.Resources>
    <DataTemplate DataType="{x:Type ViewModels:SquareViewModel}">
        <Views:SquareView />
    </DataTemplate>
</Window.Resources>

The above code will render a SquareView user control when WPF comes across a SquareViewModel (and set the DataContext on the SquareView to the SquareViewModel).

To place your view models in a view you can use a ContentPresenter (for a single ViewModel):

<ContentPresenter Content="{Binding SingleSquare}" />

In your case you will be wanting to have a collection of SquareViewModel items displayed so you will want to use the ItemsControl:

<ItemsControl ItemsSource="{Binding Squares}" />

This however won't give you your desired result as this will act like a ListBox by default. You will need apply a template to the ItemsControl to use an underlying Canvas. See this blog by Pete Brown for a possible implementation.

Good Luck!

Edit: Additional Code Example

View Models:

public class MainViewModel
{
    public IEnumerable<SquareViewModel> Squares { get; set; }

    public MainViewModel()
    {
        var squares = new List<SquareViewModel>();
        squares.Add(new SquareViewModel(15, 15,100,100, Brushes.CadetBlue, "Square One"));
        squares.Add(new SquareViewModel(75,125, 80, 80, Brushes.Indigo, "Square Two"));
        Squares = squares;
    }
}

public class SquareViewModel
{
    public int X { get; set; }
    public int Y { get; set; }
    public int Width { get; set; }
    public int Height { get; set; }
    public Brush Color { get; set; }
    public string Name { get; set; }

    public SquareViewModel(int x, int y, int width, int height, Brush color, string name)
    {
        X = x;
        Y = y;
        Width = width;
        Height = height;
        Color = color;
        Name = name;
    }
}

Views

<UserControl x:Class="MapView.Views.SquareView"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    >
    <Grid Background="{Binding Color, FallbackValue=Azure}">
        <TextBlock HorizontalAlignment="Center" VerticalAlignment="Center" Text="{Binding Name, FallbackValue=None}" />     
    </Grid>
</UserControl>

<Window x:Class="MapView.Window1"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml" 
    xmlns:ViewModels="clr-namespace:MapView.ViewModels" 
    xmlns:Views="clr-namespace:MapView.Views" Title="Window1" Height="300" Width="300">
    <Window.Resources>
        <DataTemplate DataType="{x:Type ViewModels:SquareViewModel}">
            <Views:SquareView />
        </DataTemplate>
    </Window.Resources>
    <ItemsControl ItemsSource="{Binding Squares}" >
        <ItemsControl.ItemsPanel>
            <ItemsPanelTemplate>
                <Canvas HorizontalAlignment="Stretch" VerticalAlignment="Stretch" Background="Beige" />
            </ItemsPanelTemplate>
        </ItemsControl.ItemsPanel>
        <ItemsControl.ItemContainerStyle>
            <Style TargetType="ContentPresenter">
                <Setter Property="Canvas.Left"
                    Value="{Binding X}" />
                <Setter Property="Canvas.Top"
                    Value="{Binding Y}" />
                <Setter Property="Width"
                    Value="{Binding Width}" />
                <Setter Property="Height"
                    Value="{Binding Height}" />
            </Style>
        </ItemsControl.ItemContainerStyle>
    </ItemsControl>
</Window>

And in the Window1 Constructor:

public partial class Window1 : Window
{
    public Window1()
    {
        InitializeComponent();
        DataContext = new MainViewModel();
    }
}