How is a pivot table created by Laravel?

To expand on Ben's answer (I tried to edit it but reviewers said it added too much):

To add the foreign key constraints, make sure if alpha id is unsigned, alpha_id is also unsigned in the pivot table. This migration would run after (2) in Ben's answer since it alters the table created then.

public function up()
{
    Schema::table('alpha_beta', function(Blueprint $table)
    {
        $table->foreign('alpha_id')->references('id')->on('alpha');
        $table->foreign('beta_id')->references('id')->on('beta');
    });
}

It appears as though the pivot table does need to be created manually (i.e. Laravel does not do this automatically). Here's how to do it:

1.) Create a new migration, using singular table names in alphabetical order (default):

php artisan make:migration create_alpha_beta_table --create --table=alpha_beta

2.) Inside the newly created migration, change the up function to:

public function up()
{
    Schema::create('alpha_beta', function(Blueprint $table)
    {
        $table->increments('id');
        $table->integer('alpha_id');
        $table->integer('beta_id');
    });
}

3.) Add the foreign key constraints, if desired. (I haven't gotten to that bit, yet).

---

Now to seed, say, the alpha table, using keys from beta, you can do the following in your AlphaTableSeeder:

public function run()
{
    DB::table('alpha')->delete();

    Alpha::create( array( 
        'all'           =>  'all',
        'your'          =>  'your',
        'stuff'         =>  'stuff',
    ) )->beta()->attach( $idOfYourBeta );
}

I use Jeffrey Way's Laravel-4-Generators or Laravel-5-Generators-Extended.

then you can just use this artisan command:

php artisan generate:pivot table_one table_two