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

Helper.cs

using System;
using System.IO;
using DemoLiteDB.Droid;
using Xamarin.Forms;

[assembly: Dependency(typeof(Helper))]
namespace DemoLiteDB.Droid
{
    public class Helper : IHelper
    {
        public string GetFilePath(string file)
        {
             string path = Environment.GetFolderPath(Environment.SpecialFolder.Personal);
             return Path.Combine(path, file);
        }
    }
}