Built in the the 16th century by the Emperor Akbar, Fatehpur Sikri (the City of Victory) was the capital of the Mughal Empire for about 10 years. Then it was abandonded for reasons that are still something of a mystery. It includes one of the largest mosques in India, the Jama Masjid. It is full of well preserved palaces and courtyards, and this UNESCO world heritage site is a must see for anyone visiting Agra.
Touts and scams
As you enter, you will be asked to remove your shoes, which is normal as the mosque is in use. The folks who tell you, however, will neglect to indicate that they will ask for an unofficial "fee" for watching your shoes. Don't pay! Just walk away, they will do nothing as they are in the wrong. Avoid this completely by bringing a plastic bag to carry your shoes in.
One (or more) of the people near the shoe scammers will follow you around offering to tell you about things "for free, as [he] works here". These "guides" will be ridiculously persistent... Unless you tell him a clear no (several times), expect a tip/fee request at the end of your "free tour".
Hire a car with driver from Agra (your hotel is probably the simplest, but maybe not cheapest) or getting an auto-rickshaw to get there.
Expect to pay around 1,600 Rs for an air-conditioned car booked through a hotel.
Auto-rickshaws will quote you around 800 Rs.
Given that the ride is quite long, at about 1 hour each way, the comfort of a car might be more preferable.
Fatehpur Sikri can be reached from Agra with a direct public bus from the Idgah bus station (but not the ISBT bus station) which will take you to the terminal in the center of the village just below the historical palace in roughly an hour. The fare is 40 RS. Locals say that it leaves every 30 minutes between 6am and 7pm, however only one coach seems to be in use, which goes back and forth. This reduces the actual frequency to just 1 bus every 2 hours. However, other buses in particular those connecting Jaipur to Agra, can pick you up resp. drop you off at the by-pass Junction not far from the village center. From there it's just a 5 minutes auto-rickshaw ride to the village center.