These falls are a real Disney World. The excursion to the falls is sold at hotels but the companies take people up the falls the opposite way. You climb up from the bottom (I believe going as far as the 7th fall) and then make your way down. To better appreciate the falls, we recommend you walk up the mountain and then make your way down through the falls.
Some time ago went with a group of 50 (including people who couldn't swim and a six year old girl). What you need is clothing that can get wet and dry quickly, good pair of shoes that can get wet but are rugged to walk over rocks, and wont weigh you down when you jump into a fall. Bring some snacks, but be sure they are lightweight and please dont leave any garbage.
Get a guide at the Damajagua exit of the Imbert highway. We went with Roberto and Joel, who know their stuff. There are signs on the road. You may consider renting a car as the taxi may cost you as much as renting a car for the day.
To do it right is to spend a whole day at the falls. Take the mountain road up - about two hours making stops to admire the jungle vegetation- and then make your way down the 21 falls. You will jump down the falls, or toboggan down the falls. Bring rapelling gear, just in case it has not been raining, because then the waters of some of the drops may be too shallow and you have to rapel down for safety. We did this, no problem.
It took our group a whole day -we started our climb shortly before 10 and were back at around 5 pm, but remember we were 50, so that meant we spent about two hours at the rapelling point because it was one by one.
If you are somewhat adventurous, this will be the highlight of your trip to the DR and one to remember for ever.