Exegesis:

ērxato de legein pros autous ‘then he began to say to them.’

archomai ‘to begin,’ with following infinitive occurs 27 times in Luke. In some places it clearly refers to the beginning of an act, or event (e.g. 7.15; 9.12; 14.30). In others, however, the idea of beginning is almost completely absent, and archomai apparently has only the function of an auxiliary verb; or it has no specific meaning at all and may go untranslated. In a number of cases it appears to lend special emphasis to the main verb, or indicate a change in the situation. In every occurrence the context must determine in what sense it is used. Here it refers to a turning point in the situation.

hoti has the function of a semi colon.

sēmeron peplērōtai hē graphē hautē en tois ōsin humōn ‘today this scripture passage has been fulfilled in your ears.’ For peplērōtai cf. on 1.20. Here the verb indicates that what the scripture passage says has come true and is happening now. en tois ōsin humōn may be taken (1) with hē graphē hautē ‘this scripture,’ which results in ‘the scripture in your ears,’ i.e. “the Scripture which you have heard” (Torrey, cf. Knox, Russian Synodal Bible, La Sainte Bible: Nouvelle version Segond révisée, Menge, Bruns, Willibrord), or (2) with peplērōtai ‘is fulfilled,’ which results in ‘this scripture is fulfilled in your ears’ i.e. “this Scripture has been fulfilled while you have been listening to it” (Phillips). The latter is preferable.

graphē ‘scripture passage,’ in plural ‘the scriptures.’

Translation:

This is the first passage in the Gospel where Luke records a public speech of Jesus. The translator may have to decide here what honorifics to use in rendering the speech (cf. on 1.5). Since Jesus’ general behaviour seems not to have been markedly different from that of the teachers of the law, it may be advisable to model his use of honorifics on what a religious teacher would use when speaking on an official occasion in a public place to persons of varying position, some socially his equals, some not. This may imply his using polite forms, in contrast at with what he would use in private conversation in the circle of friends or disciples. That he just has referred to his being anointed by the Spirit does not seem to be a reason for departing from this general rule.

And he began to say, or, ‘thereupon (or, and then) he said.’

This scripture has been fulfilled in your hearing, or, “this passage of scripture has come true…, as you heard it being read” (Good News Translation), ‘you have heard these words completely confirmed’ (Kele). This scripture, or, ‘this text,’ ‘this wording of scripture’ (Balinese), ‘these matters that have been written in the Holy Book’ (Kituba); and cf. on “the place where it was written” in v. 17. To be fulfilled, or, ‘to reach-its-goal’ (Bahasa Indonesia), ‘to come to realization’ (Kituba), ‘to come right’ (Sranan Tongo), ‘to hit the very spot’ (Shilluk, for John 17.12), ‘to happen really/truly.’

Quoted with permission from Reiling, J. and Swellengrebel, J.L. A Handbook on the Gospel of Luke. (UBS Handbook Series). New York: UBS, 1971. For this and other handbooks for translators see here . Make sure to also consult the Handbook on the Gospel of Mark for parallel or similar verses.