Here are the Old Rite's Seven-fold Prayers translated into English, which I had previously posted on reddit:
The Sevenfold Beginnings or the Seven-seven Rule, also known as the entrance and exiting prayers, are a series of seven prayers preformed before corporate worship or before beginning of one's own prayers. There are then repeated at the end of corporate worship or at the end of one's own prayers. Additionally, these prayers are also done when one is entering or leaving their home.
Each of the seven prayers is ended with the Sign of the Cross and then a bow from the waist, with the exception of the fourth prayer (prostration instead of waist bow) and the dismissal (essentially an eighth prayer) when a full prostration, or "Great Earthly Bow", is preformed without the Sign of the Cross.
These prayers are known as a "principle" or general rule among the Old Believers, as the texts of the prayers themselves are not a major concern: rather it is the fact that seven prayers are preformed with bows and a prostration by individual worshippers that is important.
The translation from Erie, PA of one of the standard versions of these prayers are as follows:
God be merciful to me a sinner. Bow.
Thou hast created me; Lord, have mercy on me. Bow.
I have sinned immeasurably; Lord, forgive me. (Some say: have mercy and forgive me a sinner.) Bow.
It is Truly meet* to bless thee, O Theotokos, the ever-blessed and most immaculate and the Mother of Our God. More honorable than the cherubim and more glorious than the seraphim; thee who without defilement gavest birth to God the Word, the true Mother of God, thee do we magnify. Prostration, always.
*Some do a bow from the waist here, but Erie's Old Orthodox Prayer Book makes no mention of this practice.
Glory to the Father, and to the Son, and to the Holy Spirit. Bow.
Now and ever, and unto the ages of ages. Amen. Bow.
Lord, have mercy. Lord, have mercy. Lord, bless. Bow.
Then the Dismissal:
Lord Jesus Christ, Son of God, through the prayers of They most pure Mother, by the power of the precious and life-giving Cross, through the prayers of my Guardian Angel, and of all the saints, have mercy on me and save me a sinner, for Thou art good and lovest mankind. Prostration.
Some priestless Old Believers, most notably the Нетовцы, have taken the Sevenfold Beginnings and altered its meaning to become a sort of rite that causes one to enter into the Old Orthodox faith (edit: as a replacement for baptism). But, as mentioned earlier, this is an uncommon view among the Old Believers.
(The prayer book where these prayers are found is what began my interest in the Old Rite.) Part of what I find attractive about the Old Rite is that it is more orderly (for lack of a better term), that it tends to emphasize the role of the body in prayer a little more, and that it is more aesthetically pleasing (as silly as that sounds). I don't exactly enjoy the fact that I like it for those reasons, but it is the case nonetheless.