Within the Roman Catholic Church, the normal order of progression is Baptism as an infant, first communion during elementary school, and confirmation during high school.
Within the Eastern Orthodox Church, a baby received into the Church receives all three of these Sacraments at the same time: he/or she is baptized and chrismated (analogous to RC confirmation), and then receives Communion at the first Liturgy following his or her baptism/chrismation. Usually, baptisms occur before a Liturgy, so a newly received infant receives his or her first Communion on the day of his or her baptism.
The Eastern Orthodox Church does not recognize any sacraments of any other church with the exception of Baptism. Usually, a Roman Catholic (and I believe Anglican) being received into the Church is not (re-)baptized, but this is not universal. For the purpose of your novel, however, you can probably assume this is the case.
So, again for your novel, on the day of a Roman Catholic or Anglican convert's reception into the Eastern Orthodox Church, you can expect them to be chrismated and then to receive Communion at the Liturgy following their chrismation. Usually, newly "illumined" converts are brought to the front of the communion line by their godparents and they usually hold a candle as they approach the chalice.
I am writing all of this from personal experience: I am an RC convert to Eastern Orthodoxy.
I am sure you can find videos of the actual rite on YouTube. Just make sure that you are seeing the reception of a layperson and not clergy. There is a different process for receiving RC or Anglican clergy into the Eastern Orthodox Church (where they usually begin serving as priests after they are received).
As far as adult preparation, one should expect a minimum of 6 months, maximum of 1 year of preparation, some formal, some informal. But it may stretch out for much longer, depending on the convert. I know one Baptist who took 14 years. Each week he came to the priest with a new set of questions and objections. When all of these were exhausted, he decided to be received. (He came to the church to argue with the priest over the word "Orthodox" being displayed on the church sign, as he saw the Eastern Orthodox Church as being completely at odds with "orthodox" Christianity).