The sign of the cross in Catholicism is a sacramental - a sacred sign instituted by the Holy Church which prepares the person to receive grace disposes him or her to cooperate with it. Making the sign of the Cross has been used since the very earliest days of the Church. Tertullian in roughly the year 250 AD wrote:
“In all our travels and movements, in all our coming in and going out, in putting on our shoes, at the bath, at the table, in lighting our candles, in lying down, in sitting down, whatever employment occupies us, we mark our foreheads with the sign of the cross”
And Saint Cyril of Jerusalem wrote in his Catechetical Lectures:
“Let us then not be ashamed to confess the Crucified. Be the cross our seal, made with boldness by our fingers on our brow and in everything; over the bread we eat and the cups we drink, in our comings and in our goings out; before our sleep, when we lie down and when we awake; when we are traveling, and when we are at rest”
In the 400s, during the Monophysite heresy (it denied the the Holy Trinity by denying the two natures of Christ - human and divine) this sign was formalized by placing the thumb, forefinger, and middle finger together and making the sign of the cross from the forehead to chest, right to left shoulder. The three fingers symbolized the Trinity while also forming the Greek abbreviation I X C (Iesus Christus Soter). The ring finger and pinky finger were to be bent downwards against the palm of the hand to symbolize the unity of human and divine in Christ.
Pope Innocent III updated this procedure for the Latin Rite:
“The sign of the cross is made with three fingers, because the signing is done together with the invocation of the Trinity. …This is how it is done: from above to below, and from the right to the left, because Christ descended from the heavens to the earth, and from the Jews (right) He passed to the Gentiles (left). Others, however, make the sign of the cross from the left to the right, because from misery (left) we must cross over to glory (right), just as Christ crossed over from death to life, and from Hades to Paradise. [Some priests] do it this way so that they and the people will be signing themselves in the same way. You can easily verify this– picture the priest facing the people for the blessing– when we make the sign of the cross over the people, it is from left to right….”
Lastly, Adrian Forescue and J.B. O'Connell writes in their work The Ceremonies of the Roman Rite :
“Place the left hand extended under the breast. Hold the right hand extended also. At the word Patris [Father] raise it and touch the forehead; at Filii [Son] touch the breast at a sufficient distance down, but above the left hand; at Spiritus Sancti [Holy Spirit] touch the left and right shoulders; at Amen join the hands if they are to be joined.”
When entering the church, it is customary to make the Sign of the Cross with Holy water - the three fingers of the right hand are dipped into the font and the Sign is made to remind one of their baptism and to remind one that they are entering a sacred place.