The Catholic Church, following St. Augustine (e.g., Grace and Free Will, 1,1; Sermon 169, 11,13), accepts predestination of the elect to heaven, but also affirms the freedom of the human will, thus staking out a position distinct from Calvinism. Predestination to hell, in Catholicism, always involves man's free will, and foreseen sins, so that man is ultimately responsible for his own damnation, not God (double predestination is rejected).

The Catholic Church affirms predestination as a de fide dogma (the highest level of binding theological certainty), while at the same time affirming free will and the possibility of falling away from the faith.

But, there is no official teaching on how exactly this comes into play. There are numerous theological schools of thought on the matter, the two major ones being the Thomists and the Molinists. I tend to subscribe to the former. The latter is closer to the Arminian position.

Any theological position on election, however, must conform with the Church's soteriological teachings. Molinism, Thomism, and Arminianism all conform, Calvinism does not. To conform, your theology must accept the following:

1) Free will; that is, God allows people to choose him, and allows them to reject them. People always have the option. Thus election, if you believe it, must be an act of persuasion and not compulsion.

2) Co-operation; it is necessary for salvation for a man to cooperate with God's grace. Man must continuously allow God's grace to work in him. If at any point a man prevents this, he falls from grace.

3) Jesus died for all men, and his sacrifice has the potential of saving all, but his act did not automatically save anyone, only those who choose to accept him.

4) Man is born in a state of sin, and must be called by God in order to accept Him and thus receive the merits of Christ's sacrifice.

5) God predestines no one to Hell. i.e. you can only believe in negative reprobation, not positive.

There are, of course, many other teachings on salvation, but these are the main ones. Thomism, unlike Calvinism, accepts all of them. The main difference between the various schools of thought is how the calling grace of point 4 get dispensed, and its effects. Thomists maintain that God does not bestow it on everyone, while Molinists maintain that he does.