Canonisation is a phased and formal process and procedure to declare a deceased holy person as Saint.
The minimum waiting or gestation period is five years after death. The deceased person whose name is to be declared as Saint should have very popular reputation among the followers of the church and faith.
It is the Diocese to which the person belonged who has to initiate the process of beatification and canonisation. They have to apply and get the permission of their top hierarchy for initiation of the process. There are various prescribed layers of authority for these. The first is to get the person declared as 'Servant of God. For this the dioces should start gathering all proofs and testimony of the 'miracles' performed by the deceased holy person. The testimony will be collected from the collection of writings kept in churches and in private hands amnd literature. A few suitable cause testimony will be then finalised and sent for approval. The finalisation and approval is done by the different layers or tribunals in the faith administration hierarchy.There are some designated congregations also for these. Then a due 'Decree' is is given on 'Miracle' and the person is beatified and declared as 'Blessed'.
More Miracles have to be supplemented and after a phased process of approval of all those miracles and by the top hierarchy canisation is done- entered into the list of Saints.
The list to be entered is universal, national or local depends upon the reputation and acceptance of the deceased person by the followers and faith and the geographical reputation.
What I have given is only a general info and the procedures are long and detailed, and may take many years.
(Canonisation of Sister Alphonsa of Kerala, in 2008 was an event in of first woman of Indian origin to be canonized as a saint by the Catholic Church,)