how can i take express train to dalian from taoxian airport

From both Sheyang North Railway Station and the Railway Station, you can find the direct bullet trains for DL.
From Shenyang Xiantao airport, you can find the direct shuttle buses for the north railway station and the railway station.
It is suggested to check the trains' schedule on this website and then choose the right railway station, so that you will find the right shuttle bus.