Tamsui Station is at the northern end of Taipei Metro’s red line. Most people get the metro train here from Taipei Station (38 minutes, NT$50). If coming from Xinbeitou Station in Beitou, you’ll need to transfer onto the main red line (about 30 minutes, NT$50). From the station there are many buses that head up the coast, with the main one being the R26. See the individual destination pages for exact directions to the tourist spots.
There is a YouBike station just outside Tamsui Station. If coming on your bike from elsewhere, just head up Tamsui River and you’ll eventually reach the station. Most of the sites are then a short bike ride away, although some require going up a hill for a few minutes. The area is also very walkable too, and you’ll see many people doing all the attractions just on foot, as it’s a very pleasant and relaxing way to enjoy the coastline.