At the reading of the Holy Apostle during the Divine Liturgy:
The Reader approaches the Priest or Bishop at the High Place during the time of the Trisagion, with the Apostol in his hands. Liturgical books are, when being used in the Divine Services, carried upright in both hands, the front cover facing away from the Reader as he walks; they are never carried at one’s side, under an arm, etc. (As a reminder, tonsured Readers or ordained Subdeacons must always be vested to read during a Divine Service: that is, in their cassock and stichar).
The book is presented to the Priest, who blesses the Reader and lays his hand atop the book, which the Reader in turn kisses. He then proceeds out one of the side doors into the Nave, and walks directly to the place appointed for the reading. If he arrives before the choir has finished singing, he stands with the book before him, closed, until the time comes to begin the prokeimenon, etc., at which point he opens the book and holds it always in both hands (never simply in one).
When the Reader is in the centre of the church for his reading and for the exchanges that preface it and follow it (i.e. the exchange of peace with the Priest, the prokeimenon, the alleluia), he always stands completely upright; he never makes bows during his words, nor does he make the sign of the Cross at any point there (since both hands are on the book). Similarly, he does not make a bow or any other inflection at the conclusion of his reading, but remains standing straight.
After the alleluia is complete, the Reader re-enters the Altar. If there are sufficient servers that others may take care of the affairs leading to the Gospel (the candles, etc.), the proper full practice is for the Reader to stand on the right (south) side of the Holy Table, facing it, the book held closed before him, and remain there as the introduction of the Gospel Reading takes place; only when the Deacon says ‘Let us attend…’ and the Gospel reading begins does the Reader then approach the Priest at the High Place, presenting him the book and taking a blessing once again, then stepping aside to listen solemnly to the Gospel. If, however, there are insufficient servers for this and the Reader is required also to carry a candle or perform some other service in the course of the Gospel reading, then immediately upon re-entering the Altar he may present the book to the Priest, then set it aside and carry out his additional duties.
The reading of the Old Testament:
When Old Testament or other readings are appointed (e.g. at festal Vespers), readers (whether tonsured or lay) should bring the service book into the Altar and present it to the Priest before their reading(s), then go out into the Nave to read. At the conclusion of their reading, they return to the Altar to receive another blessing.