I've been to the parts of Rome that comprise this UNESCO site twice-back in 2011 and in 2014. There's nothing quite like sitting in a taxi, heading into Rome for the first time, and rounding the corner to see the ruins of the Forum.
Today the remains are mostly a jumble of what was rescued from archeological digs. Many of the main sites were covered in 20-30 feet of dirt and debris until the 19th century.
It's been a while since I've been, so I don't have great practical tips. However, here's the interview I just conducted about the Roman Forum that goes much deeper into its history: The Roman Forum.