There's a nice choice of simpler and more challenging - but regardless, you'll want to make sure you have sturdy but comfortable walking shoes, as well as some kind of rainwear, because you may find yourself needing it!
On the easier end, the Angelito Trail takes about 20 minutes to complete and is particularly popular because it ends in a natural pool. Los Pichachos is even shorter, but steep, leading up to the El Yunque summit 1,080 metres (3,540 feet) high - obviously the views from up here are worth the effort.
If you're feeling a bit more adventurous, La Coca is about 2km (just under a half mile) long, also steep, and crosses streams which might leave you a tad muddy as it takes you to the wild Mameyes River. And the longest (at 8km, a little over a mile and a half) is El Toro, which will also take you up to the summit. El Yunque through a fairly steep path of also nearly 8 kilometers. There are areas where it is even necessary to climb rocks, but you will see all the flora of the forest. This is also the most isolated of the four, but stick to the trail, use common sense, and you'll be fine.
Read more in our post The Jewel in Puerto Rico´s Eco Crown: El Yunque Rainforest.