This is actually VERY easy to do, as the falls are within the ROYAL NATAL NATIONAL PARK, administered by Ezemvelo KZN Wildlife and you can stay in the camp TENDELE in the park.
It is possible to hike relatively easily to near the bottom of the falls (from within the park itself) and even to the very TOP of the falls (after a 1 & 1/2 hour drive from the park)!
You should bank on 2-3 hours each way to get to the top of the falls and the view is surely one of the most beautiful on earth.
A massive series of cliffs falling more than a kilometre, and four kilometres long uninterrupted.
It is magnificent.
Tugela is definitely an easy one to visit, and the park it is in is more beautiful than anything I have ever seen in the Northern Hemisphere (though other areas I have seen in South Africa certainly rival it).