Note: US Citizens require a Visa for entry in to China. Single-entry, short-stay Visas may be applied for at the border, or in Hong Kong, but it is better to get your Visa before traveling. I recommend using ZVS and applying at least 45 days in advance
For ease of travel, I recommend going to Hong Kong first, enjoying some of the sites there, then heading inland.
Already in Hong Kong? Getting to Guangzhou couldn't be easier. Here are 3 options, listed in order of ease:
1. From Hung Hom MTR station buy a ticket on the Express ($190 HKG, Cash only!).
There are twelve trains daily between the two cities. Travel time is around two hours. There is 1 stop along the way (Dong Guan).
This will drop you at Guangzhou East (Guangzhoudong) station. From here you can take a taxi to your hotel, or walk if it is located in the area (Lilac, Westin, and many others are less than 5 minutes walk away)
2. Have some money left on your Octopus Card? Take the MTR to Lo Wu station, walk across the border (clearing customs) in to Shenzhen China, then take the express train from here to Guangzhou East. This will not save you much money, and cost a lot of time, but your call.
3. There is also a Ferry service running from Hong Kong to various Mainland China ports. I have used this service to get to Zhuhai, Zhongshan, and Panyu, but never with the intent of getting to downtown Guangzhou. Panyu is a southern suburb of Guangzhou and once there you can take a bus or taxi to your destination. I would only recommend this method if you needed to visit someone in Panyu first, and they could help you arrange to get in to downtown.
Fly there - The Baiyun International Airport (CAN) has flights directly from many major cities in the Pacific Rim, but I have found that getting there from the US is more difficult. You can take a connection in Narita (Japan) or Incheon (Korea) or even Hong Kong, but with the added time, connections, and my biased preference for Honk Kong I recommend flying in to Hong Kong, staying the night, and traveling in from there there. If you do fly in, be aware that the airport is a good 30-45 minutes away from any of the major downtown area.
Stay tuned for Part 2 - What to do while in Guangzhou