Basic steps to use SQLlite in ASP.NET core 1.0 are as follows-
1) Create new ASP.NET core application

2) In project.json, add these packages-
"Microsoft.EntityFrameworkCore": "1.0.1",
"Microsoft.EntityFrameworkCore.SQlite": "1.0.1"
3) Create DatabaseContext.cs in your project-
using Microsoft.EntityFrameworkCore;
namespace AspNetCore_SQLlite
{
public class DatabaseContext : DbContext
{
protected override void OnConfiguring(DbContextOptionsBuilder optionsBuilder)
{
optionsBuilder.UseSqlite("Filename:myTestDB.db");
}
}
4) In ConfigureServices method of startup.cs, add DbContext service-
services.AddEntityFrameworkSqlite().AddDbContext<DatabaseContext>();
5) In Startup method of startup.cs, create DB like this-
using (var db = new DatabaseContext())
{
db.Database.EnsureCreated();
}
For more information, you can refer these articles-
https://docs.efproject.net/en/latest/platforms/netcore/new-db-sqlite.html
https://docs.efproject.net/en/latest/providers/sqlite/