The ruins of Babylon are about 90 kilometres south of Baghdad, on the western bank of the Euphrates near the modern town of Al Hillah. The most common way to visit is on a day trip from Baghdad, by hired car with driver — roughly two hours each way on a good road. Most travellers arrange this through a local agency, which also handles permits where needed.
The same route continues south to Karbala and An Najaf, and many tours combine all three sites in two days or a long single day. Public transport (buses and shared taxis from Baghdad) is possible but slow and not always straightforward for foreigners.
Check current security and travel advisories before going — conditions in this part of Iraq change. A guide is strongly recommended both for context and for navigating the site.