Question: As a former Roman Catholic, in the past I donated funds to have a Mass said for a dead loved one. Is there an Orthodox Christian etiquette to have a Liturgy said for a recently departed friend or candle lit?
In the Orthodox Church, we do not have the practice of doing the liturgy for a special intention... in other words, we would not do a special liturgy because someone wanted to have it devoted to prayer for a loved one, either living or dead. The Roman Catholics have such a practice (the Votive Mass), but they also have the practice of having a priest or bishop serve multiple masses in a single day, and serving those masses on the same altar. In the Orthodox Church, a Liturgy is appointed for most days of the year, but a priest can only serve it once, and a liturgy can only be served once on a given alter, and anything to the contrary is strictly forbidden.
We do have services that can be requested for specific intentions. For example, you could request your priest to serve a Pannikhida for someone who is departed, or you could request a Moleben (Paraklesis) to pray for some other specific purpose.
Within in the context of the Liturgy, there are also ways that you can pray for specific purposes. Of course you can always light a candle in conjunction with any prayer. In Russian practice, you can submit a prosphora before the Liturgy, along with a list of people that you wish to be commemorated during the Liturgy. In parishes that do not follow this practice, you could still ask the priest to commemorate specific people when he is serving Proskomedia, and he will take particles out of the loaves used for that service (the Russian practice is the same idea, it simply involves a separate loaf, which is returned to the person that submitted it, minus the particles that the priest removed). You can also ask a parish or a monastery to commemorate either the living or the date on a long term basis (or even perpetually), but one should offer a donation at least sufficient to cover the expense of the prosphoras, and also for the benefit of the parish or monastery, as an offering given to God on behalf of the person or persons you wish prayed for. For example, some people make an annual donation for this purpose, along with a list of the living and the dead they wish prayed for. For more on this, see Holy Bread in the Old and New Testaments and Stump the Priest: Commemorations.
Usually, on days other than Sunday, a Litany for the Departed can be done at a Liturgy, and so if your parish does daily Liturgies, or on Soul Saturdays, you could ask the priest to commemorate an Orthodox Christian who has departed.
There is also the Litany of Fervent Supplication at each liturgy, in which prayers can be inserted for various purposes, and so for example, you might ask the priest to do a petition for someone who is traveling or who is sick.
Of course if you are going to ask a priest to pray for someone, you should be sure to do so yourself. The idea of these practices is that you join your prayers for these people with the rest of the Church, when you submit names to be commemorated at the Proskomedia.