Very easy, when you arrive in Guangzhou Airport, please take the airport shuttle bus Line6C to reach Guangzhou East Railway Station. The bus fare is 20RMB/adult and takes about 50 minutes on the way.

The train departing from Guangzhou East Railway Station to HK Hung Hom Station takes about 2 hours and costs 190RMB.

From Hung Hom to Hong Kong Airport, you could take the bus A21 which costs 33Hk$ and one our to the airport.

Actually, this is not a good way. A suggested way is that you could take the bus departing from Guangzhou downtown area to Hong Kong Airport directly.
Please take the Guangzhou airport shuttle bus Line5 and get off at Jinhan Exhibition Center (16RMB and 45minutes). Just at the Center, you could catch a bus to HK Airport respectively at 06:30, 06:50, 07:10, 07:30, 07:50, 08:10, 08:40, 09:10, 09:40 and 10:10. The fare is CNY200 per person and the journey is about 3 hours.

If you miss the bus departing here, please go to the Marriott Hotel which is just opposite to the Jinhan Exhibition Center. There are also buses departing to HK Airport directly with a fare of CNY220. The bus schedule: 05:30, 06:30, 07:00, 08:00, 09:00, 10:00, 11:00, 12:00, 13:00, 13:30, 14:00, 15:00, 16:00 and 17:00.

Tips: why don't you fly to Shenzhen from Dalian. The airfare is the same as to Guangzhou. At Shenzhen Airport, you could take ferry (272RMB/50minutes) or bus (180RMB/2hours) to reach Hong Kong Airport.

Oh, there is flight from Hk to Guangzhou, but expensive although just one hour is needed.