The Russian phrase for “each other” is formed by saying the word друг twice in a row. The second друг occurs in a case other than the nominative, i.e. you can find these five forms:

The case of the second друг depends most often on the verb in question. If the verb requires a direct object, the second друг shows up in the accusative case; if the verb requires a dative object, the second друг shows up in the dative case. Likewise genitive — genitive, and instrumental — instrumental. Here are some examples:

If the verb requires a prepositional phrase as its complement, then the preposition comes between the two другs:

Native English speakers, of course, will be tempted to write things like «Мои сёстры постоянно сплетничают о друг друге». And truth to tell, native Russians will say or write something like that, but it is not considered good written style.

Interestingly enough, sometimes the Russians substitute дружка for the second друг. Thus you get:

That makes the phrase much more informal and conversational. For instance:

I was interested to find the phrase as well in a site devoted to Russian folk magic. Here is a spell people use to help repair a family fracas:

You'll notice that жгут, обходят and читают are not command forms but third person plural verbs. In the translation they are rendered as imperatives to make the English flow better.