Necessities:

Trees were cut down; they were used to build levers, scaffolding and foundation.

Rocks were hewn and brought back. The finest were used on the outside; on the inside they used uneven lots.

Sometimes a kind of concrete was used to strengthen the tunnels or to make them waterproof. In Germany the Romans used a combination of lime, sand, stones and water (opus caementicium in Latin).

The Romans used several instruments to map the countryside (chorobate, groma, leveling staff and dioptra) and a kind of hoisting crane + drilling machine.

In principle there are three kinds of aqueducts: masonry, lead or earthenware pipes. In Rome masonry was the most common version.

Building it:

If there was no solid topsoil the Romans drilled poles into the ground for the pillars. Then they made a kind of wickerwork of wood. On this they placed the stones. The Romans used cranes to lift heavy blocks to the top of buildings under construction, but of course they were powered by people pulling ropes.

At the top of these pillars came a mold for the arch. When ready the mold could be taken away (although they did not invent arches in buildings, the Romans were the first people to use them to construct bigger, wider buildings without having lots of rows or pillars to hold the roof up).