‘And he came to Nazareth, where he had been brought up.'
This incident took place some time after Jesus commenced preaching, as in fact Luke 4:15-16 make clear. (Some argue that we find it in Mark 6:1-6 (very much abbreviated), but that is questionable. See above). Either way Luke apparently has knowledge of what happened which was unavailable to Mark, probably because Mark's source Peter was not present, while Luke's source was (it may have been His mother). It is clear that Luke wishes to present Nazareth as a kind of official launching point of His ministry, partly because of the suitability of what Jesus said when He was in Nazareth as an introduction to His ministry, and partly because this was where the angel had declared Him to be the Son of the Most High, the Davidic king, and the Son of God (Luke 1:32-34). It may well be that the actual launching point was unknown. Alternately it may be because he wants to demonstrate immediately after the temptations how the attack of the Devil always follows blessing, resulting in a move in situation and further blessing (see especially how this pattern is brought out in the case of Paul in Acts 13-14, Acts 13:16).
(Jesus had already ministered for a period in Judaea, but that had been in support of John. He had not then wanted to diminish John and had not therefore fully identified Himself, even though John had identified Him clearly. But now that John was in prison He launched His own ministry publicly, and that is what Luke is bringing out. See John 1-4. See also Matthew 4:12; Mark 1:14 which both identify the commencement of His ministry in Galilee with the imprisonment of John.)
Nazareth was not a large town, being nestled in a valley on a mountainside, which looked out over the plain of Esdraelon. But it was as, we already know, Jesus' home town. He had grown up there and they had seen His perfect life, and had grown used to it. He was simply particularly well favoured, but He was not important. They saw what we would have given our eyes to see, but it had hardened them against the truth, just as too much of the Gospel can do the same. Too much of what is wonderful makes us lose our sense of wonder. (Everyone knows what the Gospels say, but few have ever really read them. They judge on hearsay. Others have dissected them into little bits and cannot see the forest for the trees.).
‘And he entered, as his custom was, into the synagogue on the sabbath day, and stood up to read.'
Arriving in Nazareth Jesus went on the Sabbath to the synagogue ‘as His custom was'. This may signify that it had regularly been His custom to go to the Nazareth synagogue, which we would anyway have assumed, or it may be referring to His custom on the Sabbath day to go to the nearest Synagogue as in Luke 4:15.
In the Synagogue He stood up to read. This would be at the invitation of the ruler of the Synagogue and was probably part way through the ‘service'. This is the first description that we have of a Synagogue service, but if we assume that it followed the pattern of later services it would commence with prayer, the Shema and the Blessings, followed by a reading of the Law. It is only then that someone would be called on to read from the Prophets. The Scriptures would be read in Hebrew and possibly translated into Aramaic.