Each of + determiner + plural noun = Each can be followed by a determiner (A, an, the, my, his, etc.) and a plural noun; refers to only one of a set or collection; or to a set or collection among others; hence, each takes a singular verb (‘is’) which is also a traditional choice:
Each of these pies is crispy.
Each of these kids has a talent for acting at an early age.
Each of the candidates has considerable expertise in the construction of dams.
Each of the guides has a story to tell while taking us up into the mountains.
Each of the employees in this organisation plans to take retirement before the age of 50.
She gives each of her students homework before they go for vacations.
Each of the cities has its own mayor.
Also, the words each, each one, everyone, everybody, anyone, anybody, nobody, somebody, someone, no one, either and neither are singular and take a singular verb.
Everyone has their (his or her) own ideas about how to raise funds for the poverty-stricken immigrants.
Be careful! Don’t use each in negative clauses:
Each of the documents was not credible to convince the judge. ✗
None of the documents was credible to convince the judge. √
Notice that when we speak informally, we often use a plural verb:
Each of the students have to sign the register before they leave. (Informal)
Each of + pronoun (you/us/them)
We use the pronouns you, us, them after each of:
Each of us wishes for good fortune.
Father gave each of us a small booklet at the end of the sermon.
Jessica decided to give each of them a good clean.
Each of you needs some rest before tonight’s journey.
The verb following each of + pronoun must be in the singular form.
Each (as a pronoun)
Each can be used as a pronoun (without a noun):
When the delegates entered the hall, each was given a translator. (Each = each of the delegates)
When the delegates entered the hall, each one was given a translator. (It is more common to use each one instead of each by itself).
Note: Some usage guides disagree on the usage of the pronoun [each] when it is followed by the phrase containing a plural noun or pronoun; they say the verb should be plural:
Each of the students have (or has) spoken for or against the motion.
Notice that we use they, their and them when we don’t want to be gender-specific to refer to the phrases such as ‘each candidate’, ‘each participant’, etc:
Each candidate complained that the community centre where they (he or she) were put up had the worst facilities.