There's enough Forum you and enough Forum me, this archaeological site is deceptively massive and…read morespread out, and one of the most renowned throughout Rome and the world.
Layers upon layers of history are built on top of itselves here, to the east close to the Colosseum is the Tempio di Venere e Roma (Temple of Venus and Rome), built on top of two former residences of Emperor Nero, beneath the bare mound surface is an elaborate domed rotunda. Under the Farnesian Gardens on the risen Palantine Hill belies the ancient remains of the first imperial palace (Domus Tiberiana), with soaring vaulted ceilings and deep chambers. In more than one pagan temple, churches and basilicas have been erected, Basilica di Santa Francesca Romana, Basilica dei Santi, and Tempio di Antonino e Faustina, a tribute by the emperor Antoninius Pius to his wife Faustina after her passing, later modified in the Middle Ages into Chiesa di San Lorenzo de' Speziali in Miranda.
Entry for most starts at the Arco di Tito on the eastern edge of the park, where individual and group ticket holders alike go thru security and stream in to traverse the grounds that emperors and plebes alike strode over for two to three millennia.
From there you walk west, and perhaps south then west--up the stairs to the gardens and remains of former residential quarters of antiquity. Most in-person and audio tours will take you this direction too, and I'd recommend this as a good way to learn more about the site. There are some metal info placards posted around the ruins that are helpful as well.
Plan at least one hour to walk thru just the ground level of the Forum, if you want to take your time and get to the entire Palantine Hill then three hours is more realistic.
The archaeological site has minimal shade in open areas, so bring water and maybe a hat in the warmer months; you can walk into a few of the churches or museums, including the Museo del Foro Romano, and the recently restored Domus Tiberiana (mentioned above). On top of Palantine Hill there are more trees.
My first time here I completely missed Palantine Hill and that was a mistake! This time around after an hour and a half, the park was closing and I still didn't see about half of it in as much detail as I would've liked...I guess that means there needs to be a next time!