Take highway 3 out of San Juan to the east. Highway 191 will go into El Yunque from the north side. There will be a large sign at the turnoff. This is the tourist side--where all the buses out of San Juan and from the cruise ships go. It is very pretty and has lots of tall water falls. Road 191 does not go over the mountain--it is closed at the top.
However, the south side is the explorer side--where you go if you want to be away from the tourists. Here, you want to stay at Casa Cubuy or at Robin's rainforest cabin. Here you will see water falls, petroglyphs, and much more. To get there, continue on highway 3--stop off at WallMart in Fajardo to get any needed supplies (it's right on the highway). Hightway 3 will change to toll road 53 after it turns south. A little further down take road 31 at Naguabo and then road 191. Naguabo is a little town but has several fast food places and a couple hardware stores. The highway 31 exit floods during storms and may be closed for a few hours after a hard rain.
For a detailed map--click here.