Dragonfly Dome is in the High Peaks area, a stout hike in from the east side. The guidebook rates the Regular Route as three stars, a Pinnacles classic.
Park across from the ranger station on the east side, and start hiking from the Condor Gulch trailhead. Gain a bunch of elevation, and pass the overlook. After 1.7 miles turn left at the junction with the Chalone Creek trail. In about a quarter mile you should see Dragonfly Dome just right of the trail.
There may be a bit of brush, hopefully trimmed back. Elevation gain is ~1000-1500'.
Route height is 60'. Start on a pillar with a thin crack and climb the south face along a seam which goes up and left, passing two bolts and a couple of pockets / holes.
At the top there will be a bolted anchor, with rappel rings. Look down and take in the views of the west side -- the Balconies and the backside of Machete Ridge.
You can also toprope School Daze (5.9) from here. Descend by rappel.
The thin crack reputedly takes small to medium nuts / cams, but I found protecting it a bit superfluous. I placed a brown or blue (1.5 / 2.0) tricam in one of the pockets above that. Bring a couple quickdraws for the well-camouflaged (but solid) bolts too.