Example of how to implement local database in your Xamarin.Forms applications - http://julianocustodio.com/litedb

MainPage.xaml.cs

        private async void List_Selected(object sender, SelectedItemChangedEventArgs e)
        {
            var action = await DisplayActionSheet("Atenção", "Não", "Sim", "Deletar ?");

            if (action == "Sim")
            {
                var customer = e.SelectedItem as Customer;

                Customers.Delete(customer?.Id);

                ListCustomers.ItemsSource = Customers.FindAll();
            }
        }