A number of criteria are used in such an investigation. These include an evaluation of the personal qualities of the person claiming to have had the vision(s), as to whether they are mentally balanced, sincere and honest, leading a good moral life, obedient to the authority of the Church (some in the past have proved unruly and disruptive), and willing to practice their faith in the usual way. The visions and messages conveyed are also evaluated, to see that they don't conflict with the Church's theological views, and that they lead to healthy acts of devotion and good works.
Factors that would count against recognising any such claim would include any attempt to make financial gains from it, and signs of psychological disorders in the person making the claims. Only if the event is found to meet such criteria will the Church accept public participation in acts of devotion related to the alleged apparition (the locals seem to have somewhat jumped the gun in this respect). Ultimately the Church decides to approve or condemn the event. If this is indeed the usual procedure, the church ought surely to be strongly discouraging "pilgrimages' and prayers at this site until the investigation is completed.