I created a project using Navigation Drawer template. It has ShowToast() method in SimpleViewModel so that when user press Button1, it will show a ToastPresenter which returns NewText property.

I modified the ShowToast() method to open the drawer by using following snippet code:

private void ShowToast(object parameter)
{
    IDrawerViewModel drawerViewModel = IocContainer.Current.Resolve<IDrawerViewModel>();
    if (drawerViewModel != null)
        drawerViewModel.Open(DrawerSide.Left);
}

Please note that I'm using IoCContainer class to get the instance of DrawerViewModel. The registrar is specified in the contructor of DrawerViewModel.

public DrawerViewModel()
{
    this.LeftViewModel = new NavigationViewModel();
    this.CenterViewModel = new SimpleViewModel();

    //this.Open(DrawerSide.Left);

    IocContainer.Current.RegisterInstance<IDrawerViewModel>(this);
}

After saving the changes, pressing Button1 will open the drawer.

Hope this help.