Dear Pilgrim, instead of the invocation of the priest "Blessed is our God" one says "Through the prayers of our holy Fathers, O Lord Jesus Christ our God, have mrecy on us". Then the usual beginning prayers "O Heavenly King" (if outside of Pascha), etc. through the Our Father. At the conclusion of the Our Father one says either "Through the prayers" as above, or in the Old Believer usage one says the the Jesus Prayer, instead of "For thine is the kingdom" which is only said by the priest.
Instead of the litanies of the deacon, for longer litanies (Litany of peace) one simply says 12X Lord have mercy followed by Glory...both now, and for little litanies one says 3X Lord have mercy, and then Glory...both now.
At the conclusion of your Reader's Service you again say "Through the prayers" instead of the dismissal of the priest.