In the basePage tag in XAML
you can add your view model like this
<basepage:BaseApplicationPage
DataContext="{Binding YourViewModel, Source={StaticResource Locator}}">
Make sure the you have to registered the ViewModel with the same name that you are giving in the data context. I am using MVVMlight, so ViewModel and View are registered in the 'ViewModelLocator'.
Hope this helps