What is the best way to get from Guangzhou to Macau?

It depends on where you are in GZ City. Anyway, here is my suggestion:
1. By bus: at the Provincial Bus Station, take a direct bus to ZH Gongbei first. Then cross the Gongbei border to Macau!
2. by train: you are advised to take a high-speed train (actually light rail) at GZ South Train Station to Zhuhai Station. It is within walking distance to Gongbei border, cross which you ill be in Macau!