These two–neither/nor and either/or–are known as correlative conjunctions.
Where most people get tripped up in using these conjunctions is in verb tense and pronoun usage.
Let me give you a couple of examples:
Neither my classmates nor I am aware of any upcoming tests.
Neither the students nor the teacher knows her way to the auditorium.
In both these cases, and in all cases involving neither/nor and either/or, the subject of the sentence is always the one appearing after nor/or. And in both of my examples, the subject is singular. In the first one, since the subject is I, the verb has to be the first person singular am even though the result may sound weird to the ear. In the second example, teacher is the subject so both the verb and possessive pronoun have to be singular.
Now, let’s switch things around.
Neither I nor my classmates are aware of any upcoming tests.
Neither the teacher nor the students know their way to the auditorium.
As the subjects become plural, so do the verbs and pronouns.
Clear as mud, right? Just remember to ignore everything before nor or or before choosing the proper verb and pronoun. Then the mud will disappear.