The most convenient way should be traveling by train, about 4-5 hours and tickets at CNY30.00. I think there are also regular buses between Quanzhou and Guilin. You may search that online.

If you mean Quanzhou in Fujian and Guilin in Guangxi? You can drive by yourself, the whole journey will cost 20 hours in total after traversing four provinces. The most doable way is to take trains or airplanes. But you need to make a transfer in Wuhan (Hubei)or Yingtan (Jiangxi)and then take another train to Guilin. You can make an inquiry to the air ticket office to make clear the flights from Quanzhou Jinjiang Airport to Guilin. Hope it helps. Good Luck!