[Peter Hill]

There is a very recent short thread on wedding rings that might be helpful. Here is an excerpt of my post to that thread which pertains to the betrothal service:

The ring is the token of betrothal - rings are exchanged in the betrothal service. Though these days the betrothal service is prepended to the wedding service (the crowning) and they are done together, it is the betrothal (with the exchange of rings) that is in fact the "engagement" to marry (although that engagement is unbreakable without good cause and requires a Church divorce to dissolve it.) So technically, rings have nothing to do with Orthodox marriage - only with Orthodox betrothal. The betrothal rings are what we usually think of as the wedding rings in western parlance and the big diamond/fancy engagement ring is completely out of the picture. The rubrics of the betrothal in the Russian Church suggest that the groom's ring is gold while the brides is silver, however, there is no requirement for this difference.

In the betrothal service the rings are brought to the priest ahead of time and he blesses them. At the time of the betrothal, the priest takes the rings and places the groom's ring on the bride's finger and the bride's ring on the groom's finger. Then the best man/father of the bride/godfather or some other significant person (not the priest usually) changes the rings three times so that the groom's ring ends up on the groom's finger and the bride's ring on the bride's finger. In the context of the service the right hand is used, however afterward the bride and groom can shift the rings to the left if that is the cultural norm in the country where they live.