The easy drive involves driving to the Craggy Garden parking area on the Blue Ridge Parkway. It's definitely more scenic. From there you take the Mountains to Sea Trail about a mile to the Douglas Falls trail. Then travel another couple miles to the falls. The trail to the falls is beautiful with lots of lush greenery. It is rugged and a steep climb back up. There is also another waterfall that you'll cross on the trail that's pretty interesting as it's basically a long shoot. It almost looks like the log flume ride at Dollywood.
The other way is to drive directly to the area known as Big Ivy in Barnardsville. The map below will take you to the entrance, which is about an hour and forty-five minutes from downtown Greenville. But from there you'll travel on a forestry road for another thirty minutes or so assuming you're driving as fast you can possibly drive safely. The road does hug a very steep cliff so you might want to take it a bit slower. The road dead ends at the trail head which you can't miss. It's blazed in yellow and the falls are about a half mile further. There is a great campsite just above the falls and a few others on the way to Craggy Gardens should you feel inclined to head that way.
You can find more information about the area here.