I understand this may appear like a question which was already requested, however i attempted the solutions available already.

I'm creating a program with C# and I have to save data in ways that each client has their own fresh (dynamic path) to his db. So what can I actually do so customers will not have to install extra things, but simply .Internet framework?

I learned about SQLite, however i did not really have it working.

Sql Server CE. It runs in-process and you will deploy all needed devices together with your application. Check this out article:

How to: Deploy a SQL Server Compact 3.5 Database with an Application

Update: Adding another SQL Server CE related links that I've discovered useful:

Download the SQLite .Internet data provider here after which reference System.Data.SQLite.dll from inside the application. The next example should work quickly the softball bat.

using (var connection = new SQLiteConnection("Data Source=yourfile.db;Version=3;"))
using (var command = connection.CreateCommand())
{
  connection.Open();
  command.CommandText = "select name from from sqlite_master";
  using (var reader = command.ExecuteReader())
  {
    while (reader.Read())
    {
      Console.WriteLine(Convert.String(reader["name"]));
    }
  }
}

Obviously all it will is list the tables within the specified file. When the file doesn't exist then it will likely be produced instantly not to mention there won't be any tables inside it. But, at the minimum it should work.

If I am not mistaken, c#.internet can interface having a sql database without separate server software. You'd just import system.data.sqlclient.

SQL could meet your needs, but why there's no simple method of getting began by using it is the fact that database architecture isn't a simple subject. You will find lots of great books available to enable you to get began if you opt to go down that path. It deals particularly using the syntax of MSSQL, but "T-SQL Basic principles" by Itzik Ben-Gan is really a useful one. Obviously, syntax versions between different iterations of sql are very common, and never an enormous burden knowing the idiosyncrasies from the one you will be coping with.

The state SQLite QuickStart:

http://www.sqlite.org/quickstart.html

Code samples for System.Data.Sqlite, around the original support forums:

http://sqlite.phxsoftware.com/forums/t/76.aspx

You'll find a couple of options to SQLite within the solutions for this related SO question:

Alternatives to SQLite?