Enter at the ground floor arches and head to the cavea, or the sets of stairways, just as the ancient Romans did. Seating was divided by social class: the first row was reserved for senators, the middle row was for the middle classes, and the upper part was for the plebs. In Domitian's time at the end of the first century AD, a fourth level was added that was reserved for the poor, the slaves, and the women. But there were also others to whom access was entirely forbidden, including actors, former gladiators, and even gravediggers! And don't think that the Romans simply sat wherever they liked in their appropriate level: the seats were already numbered in antiquity, just like today in football stadiums!
The Colosseum could hold up to 73,000 spectators, but amazingly the system of passages and stairwells was so efficient that it could be completely emptied in just a few minutes. Another location that was equally large for sports events and performances wasn't built until the 20th century!
In the cornice you can still see the holes where the poles were placed to support the so-called "velario", a retractable awning in colored linen and silk that was used to protect the audience from the sun and the weather and was put in motion by a sophisticated mechanism operated by hundreds of expert sailors.
The arena measures 86 x 54 meters: it was separated from the steps by a balustrade and was covered by a plank floor with sand scattered over it. Below there were a number of rooms used as cells, warehouses, and changing rooms.
FUN FACT: the first elevators in history were invented precisely here, at the Colosseum. A winch system carried the wild beasts from the basement to the arena, even ten animals at a time. With this system they could also quickly change dirty sand for some that was clean. Keep in mind that the games lasted a full day!