Is this Exposition of the Blessed Sacrament or Adoration before the Tabernacle? It sound like it might be Exposition of the Blessed Sacrament. When you enter the church, if you are able, usually the custom is to do a double genuflection (both knees) before the Blessed Sacrament and then go to your seat. You can pray as you wish for the hour, just as during adoration before the tabernacle. There are no “rules” except to be respectful of others. You can read, pray your favorite prayers or pray a Rosary or the Divine Mercy Chaplet, or just sit there and talk to Jesus. I would think that at this particular vigil you would want to offer up your prayers for the cause of Life , for an end to abortion and euthanasia and things that are against life and for the unborn babies and for the women who are having abortions (they really need them).
If you are there for the opening or closing there will be Benediction and prayers and usually a hymn.
This is really a lovely thing your church is doing. God bless you.
Here’s something you can do for adoration, especially if it is to counter the scourge of abortion: make the Holy Hour of Reparation to the Sacred Heart of Jesus. It can be done communally or individually. This booklet first came out during World War II and is still in print. I picked one up at my local Catholic bookstore for three bucks.