In exactly the same way you have added previous url parameters, a slug is no different it's just another column in the table mapped to your model.

// routes.php
Route::get('/books/{slug}', [
    'as' => 'read-book',
    'uses' => 'BooksController@read'
]);

// BooksController.php
class BooksController extends Controller
{
    public function read($slug)
    {
        $book = Book::whereSlug($slug)->first();
        return View::make('books.read')->withBook($book);
    }
}

But shouldnt the slug replace the id parameter fx.?

Or will that happen automatically?

It happens automatically if the slug exist.

Check out this tutorial I created on eloquent-sluggable: http://buildweek.com/clean-url-laravel/

Might be able to help you out.