The usual formula for beginning a confession, when it isn’t face to face, is simply to enter and kneel (or sit, some confessionals have chairs too) behind the screem.
You say something like ‘Bless me Father for I have sinned, it has been (x amount of time) since my last confession, and since then I have … (list sins).’
When I go usually the priest begins with a few words first, usually a short prayer that God will guide me to make a good confession, and then I will say the above. Sometimes (if he’s a bit rushed) he simply says something like ‘Hello’ and then waits for me to start.
You certainly don’t need to start with small talk or anything - you’re not there for a social call after all! However, if you know the priest well you can certainly say hello to him and so on before beginning.
Confessions are actually meant to be in the confessional (little room) unless there’s a good reason for them not to be. Most confessionals are set up with two chairs, one next to the priest so that you can sit face-to-face if you want, and another behind a screen if you want to stay anonymous.
You can always ask the priest if there’s any option for face-to-face confessions if that’s your preference. But the priest doesn’t have to have face-to-face confession if he doesn’t want to. Remember you receive the same grace of the sacrament and the same absolution, just as effective, either way, even if you don’t ‘feel it’ as much when it’s not face to face.
