You'll want to take a look at Casson's Ships and Seamanship in the Ancient World and Ships and Seafaring in Ancient Times, if you're looking for material. In point of fact the Romans very much had drydocks, in which larger ships might be built. But the vast majority of ships were built on land and then lowered into the water by ramps and slipways. Ships were not necessarily even built near the water, but sometimes just near whatever the source of their timber was--the New Pauly says that the Nemi ships were probably built way up in Misenum and were transported overland to the lake. Ships in the ancient world were not necessarily that large--at least warships weren't, although merchant ships could be pretty gigantic

Warships of the Classical period were built for speed and manoeuvreability. It was well understood that ships became waterlogged if they were in the water too long, which made them slower. It was therefore established practice to haul warships into drydocks to dry out whenever they were not in use, and to reduce the duration of naval campaigns if at all possible. Both Athens and Carthage had extensive military drydock complexes in which hulls were built and stored. Remains of these can be seen underneath modern buildings in Piraeus (Athens).