Write all 24 letters of the Greek alphabet on the board, accompanied with an English word producing a similar sound. For example, write "A" (alfa) as in "fAther," "B" as in "Vote," "Γ" as in "Yes" and so forth. Consult a website such as iLearnGreek.com for more on the sound of each letter.
Introduce the sounds of two consonants together. "ΜΠ" sounds like "Boat," "ΝΤ" like "Dog," "ΓΚ" like "doG" and "Τ--" as "Joust." Don't forget the "dipthongs" (vowels pronounced together), information for which you can find at websites like ibiblio: The Public's Library and Digital Archive.
Explain the concept of grammatical gender, applying to all Greek nouns and subsequently affecting adjectives, pronouns and articles. Most nouns ending in "ς" are masculine, those ending in "η" are always feminine, nouns ending in "ι," "ο" and "..." are mostly neuter, while nouns ending in "α" can be either feminine or neuter. There are several exceptions, but these simple rules apply to most words kids may encounter.
Teach the concept of cases. Every noun (and pronoun, adjective and article) has four cases in modern Greek: the nominative case (the name of a person, thing or status), the genitive case (belonging to...), the accusative case (action towards...) and the vocative case (directly addressing someone or something). Books like "Greek -- A Comprehensive Grammar of the Modern Language" by David Holton et al. can come in handy.
Show the different punctuation marks used in Greek. The period (.), comma (,), colon (:) and exclamation mark (!) are common, but Greeks use the semicolon (;) as a question mark. Instead of semi colon, Greeks have the "ano telia," a period placed near the top right of the last letter.
Introduce verbs, which are similar to English. The main difference is the different ending for the second singular and second plural person.
Start with simple sentences to introduce children to the syntax of the Greek language. The most difficult part is to teach children the alphabet and the differences in nouns, verbs and punctuation, as syntax is largely similar to English.