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

MainPage.xaml.cs

using System.Linq;
using LiteDB;
using Xamarin.Forms;

namespace DemoLiteDB
{
    public partial class MainPage : ContentPage
    {

	LiteDatabase _dataBase;
	LiteCollection<Customer> Customers;
	public MainPage()
	{
		InitializeComponent();

		_dataBase = new LiteDatabase(DependencyService.Get<IHelper>().GetFilePath("Banco.db"));
		Customers = _dataBase.GetCollection<Customer>();
		ListCustomers.ItemsSource = Customers.FindAll();
		BindingContext = this;
	}

    }
}