A very straight forward verse, starting with one of Jesus's catch phrases. This verse is the only use of the word "paradise" by Jesus.

The "verily" phrase is used frequently by Jesus as a personal signature. Its vocabulary and meaning are discussed in detail in this article.  Christ makes fun of his frequent use of it. The word translated is as "verily" is an exclamation that means "truly" or "of a truth." It is an untranslated Aramaic word that is echoed by a similar Greek word, and a good piece of evidence that Christ taught in Greek, not Aramaic.

The word translated as "verily" is the Hebrew word that means "truly" or "certainly," but it sounds like the Greek word with the same meaning. In Greek, the word also means "to reap."

The word translated as "I tell" is the most common word that means "to say," and "to speak," but it also means "to teach," which seems to be the way Christ uses it more frequently. It also has many ancillary meanings such as "to count" ("to number" or like we might say, "to recount" a story) or "to choose for yourself." Christ usually uses this word to refer to his own speaking or teaching.

The word for "you" is the indirect object form of the pronoun.  This pronoun is singular, but Jesus almost always uses the plural pronoun with this phrase. In this verse, the pronoun comes before the verb, where in almost all other cases, it follows it. The form is that of an indicated object, "to you".

The Greek word translated as "to day" is an adverb that means "for today" and "on this day."

The verb "shalt thou be" here is the common form of "to be" in Greek. It means to have a certain characteristic or remain in a certain condition. It also equates terms or assigns characteristics.  The form is the future tense, second person singular. However, it could be another Greek verb that is a form of the Greek verb "to be" the means "sent into" or "let into" where the form is not the future tense but the tense of possibility in the second or third person, "you might be let yourself in" or "he might let you in".

"With" is the Greek word that usually means "with" or a related concept such as "among" or "by the means of". It also refers to "after" or "behind" when referring to a place, time, or pursuit. This word has slightly different meanings with various forms of objects. With a singular genitive object, as here, the meaning is "in common", "along with", and "by means of".  "By means of" has a particular appeal here.

"Me" is the regular first-person pronoun in Greek in the possessive form, so "my" or "of me".

The word translated as "in" also means "within", "with," or "among."

"Paradise" is the unique Greek word here for Jesus, It is a Persian word that means an "enclosed park," "pleasure ground", but it was used specifically to refer to the private gardens of Persian kings and nobles, which were walled and to which the general public was not commonly admitted. More generally,  it means "garden", and  "orchard" but Jesus and others in the Bible commonly uses other words for those ideas.  The "let into" translated of the verb seems to fit particularly well with the idea of an enclosed royal garden. The word is introduced by are article "the private royal garden."