The Roman armies had superior weaponry and technology, so while the infantry/foot-soldiers fought and kept the enemy at a safe distance, another group of people used artillery weapons such as the scorpio, onager, and the ballista.
The scorpio is a small arrow shooting long-ranged weapon that has superior accuracy (It is derived from a Greek invention but Roman improvements made it absolutely deadly.) The Onager is like a catapult but it uses weight instead of force to hurl the stone which gives it much more momentum. The Ballista is a crossbow that is of a larger scale and shoots bolts that are much larger.
Now back to the army, the Roman foot-soldiers' (as I said before) weapons were more advanced and useful because they took ideas from other areas, like the Gladius, a short sword that was used in close combat, was an idea from the Spanish, and the armor was taken from a celtic design.
The Romans' organization excelled, they had many different officers to uphold different groups of people, like cohorts, and legions (A Century was lead by Centurions.) Romans were also paranoid, or smart at some points, they attacked the people who they thought would attack them before they got attacked, in shorter terms they attacked before they got attacked.
All of this, in a nutshell, is that Romans stole ideas and either made them better or used them against enemies so they were way more strong and prepared than their enemies. (P.S. Rome pretty much fell because of some really bad emperors.)
They kept every thing secret.
Each legion was broken up into centuries commanded by a junior officer calla centurion. There were six centuries in a cohort and 10 cohorts in a legion. There weapons were mainly a short sword, a rectangular shield, body armour and a javelin.
The discipline of the soldiers in battle gave rise to their success, allowing the generals to perform complex manoeuvres without loosing the shape or intent of the force.
The legionaries were also in charge of building bridges, roads, forts and could conduct siege warfare as well as set-piece battles. Also accompanying the Legionaries were auxiliaries. These were non-Roman soldiers recruited from other parts of the empire. These operated in blocks of 500 or 1,000 under the command of a Roman officer. They might be specialist units like the Syrian archers fighting with their favoured weapons.
Auxiliaries were paid less than legionaries and served longer but were granted Roman citizenship on discharge.