Let -- This "let" is the helping verb used to translate the Greek form of the third-person command. In English all commands are in the second person. This form is used as something like our word "must." Using "let" as the active verb, rather than a helper verb like "must," changes the subject from the third party to the second.

not . --  The negative used here is the Greek negative of a subjective opinion, commands, and requests. Here, it is part of a command.

your -- The word translated as "your" is a plural, second-person pronoun in the genitive case. This pronoun follows the noun so the possessive "of yours." Here, it is the object of the previous preposition. As an object of a preposition, the genitive indicates movement away or a position away from something.

missing "the/this"  -- (MW) The untranslated word is the Greek definite article,"the," which usually precedes a noun and, without a noun, takes the meaning of "the one." The Greek article is much closer to our demonstrative pronouns ("this," "that," "these," "those"). See this article for more. 

heart -- "Heart" is the Greek word that means "heart" both the physical organ and as the seat of emotions, which we discuss in a larger Greek context in this article here. Jesus and the Septuagint use a singular "heart" when referring to a group of people.

be -- This helping verb "be" indicates that the verb is passive. Helping or auxiliary verbs are needed to translate the Greek verb forms into English.

troubled: - "Troubled" is a verb that means means to "stir", "trouble", "agitate", "disturb", "cause relaxation of the bowels", and "trouble the mind." The opposite of being "troubled" is being at peace. Jesus used this word to describe agitation of the heart and the self.

ye -- This is from the second-person, plural form of the verb.

believe  -- The Greek word translated as "believe" does not apply to religious belief as much but trusting or relying upon other people, especially their words. Jesus usually uses it in contexts, such as the one here, that apply to trusting words.

in -- The word translated as "in" means "into" a place, "towards" as a direction, "in regards to" a subject,"up to" limits in time and measure, and "for" a purpose or object.

missing "the/this"  -- (MW) The untranslated word is the Greek definite article,"the," which usually precedes a noun and, without a noun, takes the meaning of "the one." The Greek article is much closer to our demonstrative pronouns ("this," "that," "these," "those"). See this article for more. 

God, -- The word translated as "God" means "God" and "deity." It is introduced with an article, so "the God," "the Divine" or "the divine one." Jesus often uses it this way perhaps to indicate the one God as opposed to the pagan gods.

believe  -- The Greek word translated as "believe" does not apply to religious belief as much but trusting or relying upon other people, especially their words. Jesus usually uses it in contexts, such as the one here, that apply to trusting words.

also -- 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 can be translated as "not only...but also." After words implying sameness "as."

in  -- The word translated as "unto" means "into" a place, "towards" as a direction, "in regards to" a subject,"up to" limits in time and measure, and "for" a purpose or object.

me. -- "Me" is the regular first-person pronoun in Greek as the object of the verb or preposition. As the object of a preposition, an accusative object indicates movement towards something or a position reached as a result of that movement.