How can I access SQLite with C#?

You can not connect to sqlite db using SQLProvider classes. They are for sql server. You need to use SQLite provider classes.

1. Download the appropriate distribution from http://system.data.sqlite.org/index.html/doc/trunk/www/downloads.wiki
2. Reference System.Data.SQLite.DLL in your project (this gives you the SQLiteConnection class)

3. Connect with

   SQLiteConnection connection = new SQLiteConnection(@"DbLinqProvider=Sqlite;Data Source=Database.s3db"); 
   Main main = new Main(connection);
   

See https://code.google.com/p/dblinq2007/wiki/Installation#To_use_DbLinq for details.

SQLite in C# (requires System.Data.SQLite in references)

// Required references, after installing SQLite via Nuget
using System.Data.SQLite;
using System.Data.Common;

// Example usage in code...
SQLiteConnection db = new SQLiteConnection("Data Source=C:\LocalFolder\FooBar.db;FailIfMissing=True;");
db.Open();
using (SQLiteCommand comm=db.CreateCommand()) {
  comm.CommandText = requete_sql;
  IDataReader dr=comm.ExecuteReader();
  while (dr.Read())
  {
    //...
  }
}

There's an article on MSDN magazine about just that:

http://msdn.microsoft.com/en-us/magazine/ff898405.aspx