Herbert Weir Smyth, A Greek Grammar for Colleges

a. A single consonant standing between two vowels in one word belongs with the second vowel: ἄ-γω, σο-φί-ζω.

b. Any group of consonants that can begin a word, and a group formed by a stop with μ or ν, and by μν, belongs with the second vowel: τύ-πτω, ὄ-γδοος, ἄ-στρον, ἔ-χθος; πρᾶ-γμα, ἔ-θνος, λί-μνη.

c. A group of consonants that cannot begin a word is divided between two syllables: ἄν-θος, ἐλ-πίς, ἔρ-γμα. Doubled consonants are divided: θάλατ-τα.

d. Compounds divide at the point of union: εἰσ-φέρω, προσ-φέρω; ἀν-άγω, εἰσάγω, συν-έχω. (But the ancients often wrote ἀ-νάγω, εἰ-σάγω, προ-σελθεῖν, ἐ-ξάγω, δυ-σάρεστος.)

e. ς, when followed by one or more consonants, is either attached to the preceding vowel (ἄ-ρισ-τος), or, with the consonant, begins the following syllable (ἄ-ρι-στος). (The ancients were not consistent, and there is evidence for the pronunciation ἄ-ρισ-στος.)

f. The ancients divided ἐκ τούτου as ἐ-κ τού-του. This practice is now abandoned.