What is the best way to go from Guangzhou airport to hong kong?

I suggest you take the airport shuttle bus line 6 to its terminal - Tianhe Terminal of Guangzhou Airport (CITIC Plaza), close to the local East Railway Station. Then at this train station, you can take a direct train to Hung Hom, HK.

Take the metro (Line 3) from Guangzhou Airport (CAN) to Guangzhou East Railway Station (10 stops). Then take the high-speed train to HK (Guangzhou-Kowloon).
To find the metro in the Guangzhou airport, go down the escalators from your exit and follow the signs to the metro. You'll need to buy a token from the machines. Once at the Guangzhou East Railway Station, find the exit that goes to the train station and follow the signs that say Guangzhou-Kowloon. You'll buy your ticket on the second floor and from there take the big escalator up to the waiting area.