The Quran is divided into 114 suras, conventionally translated chapters, each made up of numbered ayat, verses. The suras are not in the order Muslims believe them to have been revealed. After the short opening prayer, al-Fatiha, they run in rough order of decreasing length, from al-Baqara at 286 verses down to suras of three lines near the end. The effect is that the earliest material sits mostly at the back of the book and the latest mostly at the front, which is why a reader working front to back is not reading a chronology of Muhammad's career.
Every sura is classed Meccan or Medinan. The division is not primarily about place but about time: material held to have been revealed before the hijra, the migration to Medina in 622 CE, is Meccan, and material after it is Medinan, so a passage revealed at Mecca during the conquest in 630 is counted Medinan. The classifications come from the exegetical tradition rather than from the text, and a number of suras are held to be mixed. The two bodies of material read differently. The Meccan suras are shorter, more rhythmic, heavily concerned with the oneness of God, the resurrection and the judgement. The Medinan suras are longer and more prosaic, and carry most of the legal, communal and military material.
Cutting across the suras is a second division into thirty juz, made purely for reading a section a night through Ramadan, and further into sixtieths. Verse numbering is not quite universal: several counting traditions split the text slightly differently, which is why the total is variously given as 6,236 verses and other close figures.