Whats the fastest and easiest way to go to Guangzhou from HKG?

It is recommended to take the direct through train from Hung Hom Station to Guangzhou East Station in around 2 hours.

Thanks. What time is the last train depart from airport at evenings?

I thought you simply referred to HK by HKG. Then you can take airport shuttle bus no. A21 from HKIA to Hung Hom Station in around an hour to catch the train. The last train departs at 20:01.

For a direct travel from HKIA to Guangzhou, you can also take a direct cross-border coach. It takes around 4h to Guangzhou and the fee is 250HKD per person.