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"the" takes the form of a prefix: "ה-" (pronounced "ha-")
מכתב = A letter.
המכתב = The letter.
As for "with", basically the word "עם" (pronounced "eem") is a direct translation:
עוגה עם צימוקים = Cake with raisins.
A notable exception is when "With" means "in a xyzful manner" in which case you'd use the "ב-" prefix (literally "in -").
התלהבות = enthusiasm
בהתלהבות = with enthusiasm
Generally speaking, the Hebrew "עם" covers most of the uses of "with".
While some cases call for other structures, the easy solution of "עם" is considered proper in 99% of the time (excluding the exception above).
