What is the cheapest way to travel from Hong Kong to Guangzhou?

Well, taking the direct long-distance bus is a cheap way.
There are several pick-up stations in HK, such as Ocean Park, Wan Chai, Prince Edward Station, Mong Kok, Tsuen Wan, Jordan Station.
It takes around 3.5 hours on the way. The ticket fare is about 100 HKD per person.
You can buy the tickets at subway stations and many 7-Eleven convenient stores (for buses operated by ChinaLink Bus Company).
By the way, where is your location? I can find the nearest pick-up station for you.