(For those just tuning in: I'm replying to a series of questions from a student about Catholic beliefs and practices. She'd heard that I recently became a Catholic and, reassessing her own faith journey, visited a Catholic church and sent me a long list of questions)
Is there a right and a wrong way to cross oneself? And why do people touch their forehead, eyes and mouth at one point in the service?
Yes, there is. Roman Catholics use the right hand fingertips to touch, in sequence, the forehead, chest, left shoulder, then the right, while saying "In the name of the Father, and of the Son, and of the Holy Spirit." It is, in a way, a brief Trinitarian prayer that also affirms the centrality of the cross. It can be a challenge for left-handers like myself! Greek Orthodox Christians touch the forehead and chest, but then the right shoulder first, then the left, and then bow deeply.
The use of the body, by the way, in kneeling, crossing, standing and so on is a way to get the entire person involved in worship - just like in the Old Testament. It is this continuity with the practices of the ancient Hebrews that I find interesting.
The other touching you describe comes with the announcement of the Gospel reading. It shows particular reverence for the Gospels where we read about Jesus and hear His actual words. Notice how only the priest is permitted to read it (the lay lectors can't), and how he carries the Book of the Gospels aloft from the altar to the podium while the congregation stands and sings "Alleluia". In some parishes, the altar servers flank the podium with lit candles, another symbolic act that displays special regard for the Gospels. People respond to this precious opportunity to hear Christ Himself by touching the right thumb to the forehead (an act that asks for the Word to illuminate our minds), the lips (that we may speak the Word aright to others) and the heart (that the Word of God and the Living Word, Christ, would dwell in our hearts). These parts are not just touched with the thumb tip but the thumb makes a tiny sign of the cross on those three places and the person says, "Glory to you, O Lord." As with all practices, many do it rotely without much thought. But for converts and anyone who is aware, it's a deeply meaningful prayer.