People typically bring a book or two of devotional or spiritual reading or they may just sit and mentally converse with God.
I began doing this a month or so ago and now I am addicted. When I arrive, I feel like I'm in a hurry about something. It feels very strange then to just sit there and hear nothing and do nothing. But the calm/peace comes over me pretty quickly and I just let my mind wander, talking to God about this, that, or the other thing. The hour passes pretty quickly. You certainly don't need to stay for an hour but time flies!
By the way, when you enter, most people get down on both knees, i.e. they don't do a simple genuflection. I think after Vatican II it was changed (I know, I know) so that is no longer necessary but just because something is not necessary doesn't mean it isn't worth doing.
Then, about 15 minutes before the end of Adoration, the Benediction begins.
At our parish, we say the Divine Mercy Chaplet. If Father Carroll
leads the chaplet, we may get one of his wonderful homilies. Then, we sing Tantun Ergo (in Latin!!!)* and say the Divine Praises (in English)**. Then we sing "Holy God, We Praise Thy Name". Finally, the priest puts on a humeral veil and picks up the monstrance, turns to face those of us in the pews and blesses us by raising and lowering the monstrance 3 times (while a lay person incenses the monstrance).
After the blessing the priest replaces the blessed sacrament in the tabernacle (the Reposition) and genuflects.
The first time I attended the Benediction, I walked out in a daze. It
was so beautiful and holy. Now, I try to attend whenever possible.
It's on a Saturday at our church so it's a little challenging to get to sometimes...
* Tantum Ergo
Tantum ergo Sacramentum
Et antiquum documentum
Novo cedat ritui:
Praestet fides supplementum
Laus et iubilatio,
Salus, honor, virtus quoque
Sit et benedictio:
Procedenti ab utroque
Compar sit laudatio.
** The Divine Praises
Blessed be God.
Blessed be His Holy Name.
Blessed be Jesus Christ, true God and true man.
Blessed be the name of Jesus.
Blessed be His Most Sacred Heart.
Blessed be His Most Precious Blood.
Blessed be Jesus in the Most Holy Sacrament of the Altar.
Blessed be the Holy Spirit, the Paraclete.
Blessed be the great Mother of God, Mary most holy.
Blessed be her holy and Immaculate Conception.
Blessed be her glorious Assumption.
Blessed be the name of Mary, Virgin and Mother.
Blessed be Saint Joseph, her most chaste spouse.
Blessed be God in His angels and in His Saints.