Though the Nelder Grove is 18 miles (29 km) from Yosemite's south entrance, it's not difficult to find:
1) Take Highway 41 south (marked in blue here) from the Yosemite entrance for 10 miles (16 km) to the Road 632 turnoff. Watch for the sign for the Sierra Sky Ranch Inn, which is easier to spot than the road sign. If you're arriving from the south, it'll be 4 miles (6.4 km) north of the Highway 41/49 intersection in Oakhurst.
2) Take Road 632 (marked in red) 7 miles (11 km) to the Nelder Grove turnoff. Turn left onto this unpaved road, which is officially known as 6S47Y but labeled Nelder Grove on the sign.
3) Take 6S47Y (marked in yellow) until it ends at a fork in just over a mile.
4a) To go to the Shadow of the Giants Trail, turn left at the fork and proceed half a mile (marked in orange) to the trailhead, which will be up a steepish driveway to your right.
4b) To go to all the other trails, turn right at the fork and proceed 0.3 miles (marked in a sort of turquoise) until you reach another fork. Turn left (uphill) at this fork and go another 0.3 miles (marked in purple on the map) to reach the interpretive center at the edge of Nelder Campground.
Road 632 (the red stretch on the map) is paved but winding. Traffic is generally moving in the 20 - 30 mph range here.
Road 6S47Y, the unpaved mile of road in yellow, generally doesn't get deeply rutted but is prone to washboarding. The half-mile stretches of road beyond 6S47Y can get muddy or deeply rutted. If one of these roads is in too rough of shape for your car to handle, remember that you're only half a mile from the trailheads and it shouldn't be too troublesome to park and walk the rest of the way.
The route to the grove - particularly the unpaved parts - is sometimes impassable in the winter. Soon after you turn on to the Sky Ranch Road (642), you'll pass a sign indicating that there's no snow removal beyond this point. Whether or not you can reach the grove in the winter will likely depend on how wet the winter's been and how recently there's been a storm.
As you drive up Road 632, you'll pass some burned areas. These are from the June 2015 Sky Fire, which started with a car fire and ended up burning 500 acres. Cal Fire is reluctant to let photographers wander around in the midst of wildfires, but this one was plainly visible from my house, roughly 10 miles away, so you can see some photos of the fire in progress. (Unless you're on a tiny screen, you should be able to click on the photos to see larger versions.)
Notes on the Nelder Campground area: the Nelder Grove interpretive center, marked by two cabins and a topographical model, has room for a couple cars to park. The Big Ed Tree trailhead is here, just beyond the topo model. Drive a tenth of a mile past the interpretive center to find a large parking area and the trailheads for the Chimney Tree and Graveyard of the Giants trails. Drive another tenth of a mile to reach the trailhead and parking for the Bull Buck trail.
The Sierra Sky Ranch sign has been replaced since this street view was taken, but the new one is probably even easier to spot. This view shows the approach form the north (i.e, from Yosemite). On the map above, this is the turn from the blue stretch onto the red one.
Turn left here. A sign announces the turnoff, but it's out of sight around the corner behind you here. On the map above, this is the turnoff from the red stretch onto the yellow one.