There is parking on the A5 next to the Swallow Falls Hotel, and a series of viewpoints along the road and from the hotel grounds on the south bank of the River Llugwy. Even better is to follow the footpaths across the A5 and approach the falls on foot from the north bank.
Though most of the visitor traffic is in summer, that is not really the best time to view the falls, for the heavy summer foliage can diminish the impact of the natural beauty slightly. If you can, come in the spring or autumn, when the foliage is not so dense (or even in winter, when there won't be much at all!).
A bit of history
Swallow Falls was given by the 2nd Lord Ancaster to the Betws-y-Coed council in 1913. The income from visitor fees enabled the council to pay off the cost of bringing electricity to the village! Once the debt was paid off the council passed on the benefit, and the residents paid among the lowest taxes in the country as a result.
Note
Admission fee payable, open all day, every day, as of this writing.