There are a number of waterfalls in Olympic National Park that are fairly easy to get to, and Madison Falls is one of the easiest to get to. There is a paved trail leading right to the falls, and the trail is very short. As you walk along the trail, pay attention to all of the different plant life around you. There is a multitude of ferns, along with a number of different flowering plants.
Madison Falls is taller than it looks in the picture. The view is rather deceiving. There may also be more to the waterfall than can be seen from the platform, but that platform prevents any movement. This is probably a good thing, as otherwise man-made erosion take its toll. The area is extremely beautiful, and should be kept that way.
1) From Port Angeles, take US-101 heading west.
2) Turn left on Hot Springs Road, heading south. Head a short distance to the parking are for Madison Falls, which I believe is clearly marked. This parking area is right before the fee collection booth for the park, so there is no fee to view the falls.
3) Follow the trail to the falls.
Where in the World is Madison Falls?: map