You can also take the train, although the pullman is faster is more reliable according to everyone I spoke to in Palermo. There is a stop on the train line that deposits you at the site, but, considering that my coach bus went faster than the train at times (the route the bus takes is parallel to that of the train's), it might better to stick with the bus. You can buy the bus ticket right on the bus from the driver, and all of the buses congregate near the train station. A round trip ticket was about 15 euro, I believe, although prices vary. Several coach companies operated between Palermo and Agrigento. You'll have to pay in cash, too, most likely. Some of the companies had ticket kiosks (where perhaps you can pay with credit card?), but since the price of the ticket is relatively inexpensive, cash might be the better way to go.
Make sure that you buy your return coach bus ticket at the same time (andata e ritorno). This is important because seats on the bus are first come/first serve. This doesn't guarantee you a seat on the bus back, but it will save you from having to wait to buy a ticket. Try to get to the coach bus ten to fifteen minutes early to ensure that you get a seat. The bus was fuller going back to Palermo than it was going to Agrigento. If for some reason you don't get a seat back (which would surprise me), many of the coach companies run buses all day. As long as you can buy a ticket, it doesn't matter which bus you take back. The ticket you buy will be good for any seat on that line.
Oh, and another word of advice. The tickets are just slips of paper. A part of mine "fell off" from being in my pocket, and the return trip driver almost made me buy another ticket until I found it in my pocket (albeit very soggy from sweating in the summer heat). I didn't even realize that there were two parts to the ticket, so just have a good look at the ticket. Some companies give you one ticket that can be punched twice, while others will give you a ticket that has two perforated sides (each side for each journey). I say this because my pleas of "But I bought a round trip ticket in Palermo..." had no sway with the driver, although, once he realized my confusion, showed me the ticket and how it worked.
You might be thinking that the bus will be uncomfortable, but the pullman I took to Agrigento was clean, comfortable, quiet and air-conditioned. A friend of mine took the train once and told me that it has no air-conditioning. In the hot Sicilian heat, you'll probably want an air-conditioned bus.
If you take the pullman, you'll arrive in a sort of sketchy part of town -- not criminally sketchy but where is the bus station and why are you dropping me off on the side of the road sketchy. The bus literally drops you off at this tiny run-down section with nowhere to sit and almost no one to ask for directions. Cars are flying past you as you stand only a few inches from the road. (It looked as if they were building some sort of bus depot/waiting area -- I hope it is done the next time I go back). I think that the local bus makes stops nearby, but I never saw one, so I hoofed it up to the main train station (about a 10 minute walk) and asked for directions. Inside the train station is a tourist information booth, and the people who work it are very friendly. I have to admit that I get nervous speaking Italian, especially when I am alone. The woman who helped me was really friendly and patient and explained to me which bus to take and where to take it. At one point I seemed a little "dazed and confused", and she began to speak English to help me.
Outside the main train station was the local bus stop. This bus takes you around the Agrigento area and makes a stop at the archeological park. I could say "just follow the crowds" since a lot of people were doing what I was doing -- hoofing it up from where the coach buses drop you off to the train station, buying the bus tickets and then waiting for the bus. You have to buy your ticket from one of the tobacco shops (if you're in the main train station, there is one right across from the info booth). Remember, you must buy TWO tickets -- one to get you to the archeological park and one to bring you back. There is a tobacco shop at the park, but it was closed for lunch when I arrived so it is best to buy your tickets beforehand to avoid having to walk all the way back! There are three or four buses that run past the archeological park, so you don't have to wait long. Just be sure to get off at the right stop. If you're confused, just ask the bus driver!
The return trip to town was a bit tricky as I wasn't sure where to get off since the bus route I took back was a different one from what I took there. That's not a problem, but as the bus meandered through the city center, I wasn't sure where I was or which stop would put me closest to the train station or where the coach buses all congregated. Before I forget...make sure you get on the right bus line back to Palermo.
My only "regret" was that I didn't spend the night, because I think that it would have been fun to go back in the morning and see some things that I didn't get to see as well as take some photos in a different light. Plus, after hiking around the park (it is HUGE!) all day in the hot sun, all I really wanted to do at the end of the day was drink a gallon of water, have a light meal and SLEEP! Most of my friends in Palermo said there wasn't much to see and do, but I figured I could have entertained myself for an evening...