Pine Mountain can be easily reached via a series of trails, with options for loops.
The trailhead is across the creek at the Salt Flat CG. You may have to look into the trees to see it.
Walk past the gate and follow the Willow Trail (#156) southeast for about 2.5-2.7 miles (all mileages are taken from some USFS maps, plus what the signs mention, which are not always in agreement). About a half mile in you come to some old apple trees, stone walls and some wooden ruins of somesort - this is the old Nelson Place homestead. A natural spring flows here and the creek will probably have water in it.
Stay on the Willow Trail to a junction. The signs to Pine Mountain say to turn right, but you could also stay straight (on Trail 12) and access the peak that way, too. I stayed south on #156 as it gained to a saddle at 'Cloverleaf' Junction. Turn left (east) onto Trail #14 for about 1.3 miles to the Verde Rim Trail (#161).
There are four distinct peaks on the summit ridge, each enclosed in a 6,800-foot contour. The southernmost is an easy 5-minute walk south from the 14-161 junction. The next one north is a small bump, but with open views. The two northernmost summits are about equal in height; the trail skirts both but rugged paths lead to the top of each. The northernmost summit has the "Wild" benchmark, and features a nice little meadow at the top. To the east, the Verde River Valley is a good 3,000 feet down below.
I continued north and descended sharply to the Trail 12 junction, then went west and caught up with the 156 trail, and back out.
The map I have provided is based on the USFS maps, and should be used as a rough guide only. All trails are well maintained (scant in just a few spots), and all junctions well-signed. My loop route covered about 10 miles and 1,700 feet of gain. Allow 4-7 hours.
This is bear and lion country. Just use common sense. Just the usual hiking clothes, water, maps, etc.