Hong Kong airport To Guangzhou

The most convenient way to go from HK airport to Guangzhou is to take the Airport mainland coach services.
Regular services depart from the airport between 7 am to 11 pm.
Usually, it takes around 3 hr. to arrive in Guangzhou.
You can buy the tickets from Arrivals Hall.
Detail from the HK Airport linkage:
http://www.hongkongairport.com/eng/cbt/cross.html
There is mainly 3 service providers providing cross border coach service.

Tips:
If you just want to go to Guangzhou and have no interest to visit HK, then definitely, take the airport coach is the most convenient way of going to China.
Yet, it is relatively more expensive, as generally, it cost HK$250 per ticket.
If you have plenty of time, or say, you arrive in HK in the morning, and if you would like to take a look at the HK city for a day, to do some shopping and then go to Guangzhou in the evening, then one of the alternative is to take the general bus to the city center and then take the coach from city to Guangzhou, which generally cost less than HK$100.
One of the possible route is to take the City Bus, say, no. E11, get off at stop Vicwood Plaza, Connaught Road Central. The ticket cost HK$21, the trip takes around half an hr.
If you get off at stop Vicwood Plaza, you can go to the China Travel Tours Transportation Service HK ltd, which is just next to the bus stop. If you buy the ticket to Guangzhou, they would allow you to store the luggage in their office and you can spend one day in seeing the CBD of HK and then get coach to Guangzhou, from Central.