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.