When someone wants to become a Catholic, the normal procedure is to make an appointment to go and see your local Catholic priest. You can try and get him after Sunday Mass, but he might be busy then, so it is probably better to telephone. When you see him, he will make you welcome and invite you to talk about your desire to become a Catholic.
What happens next depends partly on local circumstances, partly on how much faith background you have and of what type. Many parishes have a small group of Catholics and “enquirers” meeting together once a week for several months or longer to explore what being a Catholic means. At the end of this process, known as the RCIA (Rite of Christian Initiation of Adults) those who wish and are ready become Catholics, usually at Easter.
Other parishes do not have the RCIA, and arrange for one-to-one conversations with a priest or catechist. The needs of the enquirer are naturally paramount. You are welcome to begin attending Mass at your local Catholic Church whenever you wish, though you would not be able to receive communion yet.
You are free to approach any priest anywhere, but it makes sense to go to your local Church, which will be most convenient for you if you do decide to become a Catholic.