Walking is a great way to explore Rome, especially since many of the sights are in close proximity to each other. Other options include public transit, such as the bus or metro, but these can be crowded during peak times. Expect to pay €1.50-€2 per ride.
It's worth it to get the Roma Pass, which provides free entry to two sites, discounts at others, and unlimited public transport for €38. Add or subtract days from this itinerary as necessary, depending on your interests and pace.