The Catechism for a good start:
31 Created in God’s image and called to know and love him, the person who seeks God discovers certain ways of coming to know him. These are also called proofs for the existence of God, not in the sense of proofs in the natural sciences, but rather in the sense of “converging and convincing arguments”, which allow us to attain certainty about the truth. These “ways” of approaching God from creation have a twofold point of departure: the physical world, and the human person.
32 The world: starting from movement, becoming, contingency, and the world’s order and beauty, one can come to a knowledge of God as the origin and the end of the universe.
As St. Paul says of the Gentiles: For what can be known about God is plain to them, because God has shown it to them. Ever since the creation of the world his invisible nature, namely, his eternal power and deity, has been clearly perceived in the things that have been made. [7]
35 Man’s faculties [reason] make him capable of coming to a knowledge of the existence of a personal God.
36 “Our holy mother, the Church, holds and teaches that God, the first principle and last end of all things, can be known with certainty from the created world by the natural light of human reason.” [11] Without this capacity, man would not be able to welcome God’s revelation. Man has this capacity because he is created “in the image of God”. [12]