Most of the time I have confessed face-to-face, sitting and facing the priest (I'm a Vatican II baby, as is anyone under the age of 50). There is also the option to confess behind a screen. Older churches have three "stalls," for lack of a better word, and the priest sits in the middle. One side has an open window for face to face, and the other has a screen. The only time I've done screen, the screen was a like a thick sheer curtain where you can see shadows but nothing else. New churches have a room, where the person can either kneel behind a screen and the priest sits where he can't see who enters, or you can walk around the screen and sit in a chair. And since the sex abuse scandals, many confessionals (maybe all) have a window in the door so although you can see who's in there (and what they're doing), you can't hear what's being said.
There is the "Forgive me father for I have sinned. It has been X long since my last confession" part, then you go to it. Some churches have a little "examination of conscience" card you can look at before you go in. Some of these are pretty strict, and others are not as much, depending on which church-related organization prints the cards (some organizations will have you think it's a sin to breathe other people's air or read the horoscope in the newspaper, others are much more real world). After the sins are confessed, the priests I've confessed to will usually provide some words of encouragement and hopefully to "knock that shit off." There's an element of counseling, especially if someone makes an appointment to confess in the priest's office. "Penance" is meant to be helpful rather than punitive; and most priests I've used will suggest pertinent readings rather than "100 Hail Mary's" or whatever.
Theologically, God has forgiven the sins the minute we ask, and we don't need to see a priest for God to forgive the sins. Confessing to a priest not only shows we're (hopefully) willing to change our ways, but it restores our relationship to the church even if the relationship to God has already been mended by an inward confession.
As for anything that's illegal, including murder, the priest cannot be made to testify in court and is under no obligation to report what he's heard. What he can do, however, is encourage the person to turn himself in. I'm told there are only three sins a priest cannot forgive, but a bishop can: sins against a priest, sins against the pope, and (this is just one of those Catholic things that doesn't always make sense) abortion. Murder, rape, incest, molestation, yes, but abortion, no.