And -- The Greek word translated as "and" is used as the conjunction "and", but it also is used to add emphasis ("also"). In a series, it is best translated as "not only...but also." After words implying sameness "as".

they -- This is from the third-person, plural form of the following verb.

shall -- This helping verb "shall" indicates that the following verb is the future tense. Helping or auxiliary verbs are needed to translate the Greek verb forms into English.

say -- "They shall say" is from the Greek verb that means "to say" and "to speak" also. The form is the future tense. Luke 17:21 was also the future tense, but a negative. The quotes in Matthew are in the form of something that might happen 

to -- This word "to" comes from the dative case of the following word that requires the addition of a preposition in English, but the translator must decide which preposition to use: a "to" as an indirect object,

you, -- The Greek pronoun "you" here is plural and in the form of an indirect object, "to you", "for you", etc. ,

See -- "See" is a verb/adverb meaning "Lo! Behold!" and "See there!"  "Look!" or "See!" comes closest in English. In the related verses it is translated as "lo" or "behold" not "see".

here; - The word translated as "here" means in manner, "in this way," referring to manner, or "here," referring to place. In this verse, it follows the "there".

or, -- "Or" is translated from a Greek word that means primarily "or" but serves as "than" in a comparison.

see -- "See" is a verb/adverb meaning "Lo! Behold!" and "See there!"  "Look!" or "See!" comes closest in English. In the related verses it is translated as "lo" or "behold" not "see".

there: -- "There" is a word meaning "there", "in that place," and in philosophy means "the intelligible world." It comes before the "here" in this verse.

go -- (WM) The Greek verb translated as  "go...after" means "to go away," "to depart from", "to spread abroad," and "to depart from life."  This is a play on words because this form of "depart" is used to mean "depart from life". It is not a command, but a form of possibility, "you might depart".

not -- The negative used here is the Greek negative of a subjective opinion, commands, and requests. The sense is that "you don't want" to do something, not that it isn't done or don't think something that might be true. If it wasn't done or wasn't true, the objective negative of fact would be used. The sense here is "you might not want to depart."

after -- (WW) This prep/adverb is from the verb's prefix but the prefix means "from" not "after."

them,  -- (IW) There are no Greek words that can be translated as "them" in the source we use today nor was there one in the source that the KJV translators used. If the previous word was correct, this word would be fine because pronouns are often assumed in Greek when required in English, but since the preposition was wrong, this word is wrong.

nor -- The word for "nor" is the Greek subjective negative plus the Greek word for "but."

follow -- (CW) The word translated as "follow" means both "chase away" and "seek after." This verb is almost always translated as "persecute" in the NT, most often in the context of persecuting prophets and followers.  The English idea "hound" comes close. This is not the word usually translated as "follow." 

them.  -- There is no "them" here in the Greek, but it is implied by the previous verb. -- There is no Greek pronoun here, but Greek does not need pronouns when the object can be assumed from the context. In English, they are added for the subject-verb-object form of our sentences.