What is the proper way to do this?
Do Código Elétrico Nacional de 2017:
(C) Nongrounding Receptacle Replacement or Branch Circuit Extensions. The equipment grounding conductor of a grounding-type receptacle or a branch-circuit extension shall be permitted to be connected to any of the following: (1) Any accessible point on the grounding electrode system as described in 250.50 (2) Any accessible point on the grounding electrode conductor (3) The equipment grounding terminal bar within the enclosure where the branch circuit for the receptacle or branch circuit originates (4) An equipment grounding conductor that is part of another branch circuit that originates from the enclosure where the branch circuit for the receptacle or branch circuit originates (5) For grounded systems, the grounded service conductor within the service equipment enclosure (6) For ungrounded systems, the grounding terminal bar within the service equipment enclosure
Does the wire need to follow the same path as the ungrounded 2 wire path?
Não, não é obrigatório, mas se o fosse, seria preferível.
How would the ground enter the junction box?
Ele poderia ser pescado em outra abertura com um grampo de cabo.
How is it secured?
Para o terminal de aterramento do receptáculo de aterramento e para a caixa, se for de metal, por meio de um parafuso de aterramento 10-32.
Existem muitas maneiras de conseguir isso. Estes são os métodos preferidos do comércio, mas existem outras formas aceitáveis.
Boa sorte!