The best way is to handle this is to create a rich join table. 
Ie: 
       |  has many =>  |        |  <= has many  |
Person |               | Credit |               | Movie
       | <= belongs to |        | belongs to => |
Where Person and Movie don't change much from the initial example. And Credit contains more fields than just person_id, and movie_id. The extra fields for Credit would be role, and character. 
Then it's just a has many through relationship. However we can add extra associations to get more detail. Keeping with the movies example:
class Person < ActiveRecord::Base
  has_many :credits
  has_many :movies, :through => :credits, :unique => true
  has_many :acting_credits, :class_name => "Credit",
    :condition => "role = 'Actor'"
  has_many :acting_projects, :class_name => "Movie",
    :through => :acting_credits
  has_many :writing_credits, :class_name => "Credit", 
    :condition => "role = 'Writer'"
  has_many :writing_projects, :class_name => "Movie",
    :through => :writing_credits
end 
class Credit < ActiveRecord::Base
  belongs_to :person
  belongs_to :movie
end
class Movie < ActiveRecord::Base
  has_many :credits
  has_many :people, :through => :credits, :unique => true
  has_many :acting_credits, :class_name => "Credit",
   :condition => "role = 'Actor'"
  has_many :actors, :class_name => "Person", :through => :acting_credits
  has_many :writing_credits, :class_name => "Credit", 
   :condition => "role = 'Writer'"
  has_many :writers, :class_name => "Person", :through => :writing_credits
end
With all those extra associations. Each of the following is only one SQL query:
@movie.actors  # => People who acted in @movie
@movie.writers # => People who wrote the script for @movie
@person.movies # => All Movies @person was involved with
@person.acting_projects # => All Movies that @person acted in