Junction Peak (4233m, 36.69150N / 118.3645W) is only 1km from Forester Pass (4017m), which is on the John Muir trail, not far from Shepherd Pass (3672m), but not easy to climb.

The safest way is to climb from Forester Pass. If you are coming from Shepherd Pass, go straight west until you hit the John Muir trail (or take a short cut through Corner Lake) and turn right into this very popular trail. After moving relatively straight towards northeast, the trail will begin very steep switchbacks. Leave the trail here and go right (east) towards the saddle between the peak to the east of Forester Pass and Junction Peak. The west face of Junction Peak is not trivial, but you can always find a route that is class 3 or less, with little or no exposure.

The most popular route, instead, is the southern route from Shepherd Pass via the Diamond Mesa (which in turn is best climbed by taking it at the southeast corner, northwest of Shepherd Pass). The Diamond Mesa's north end is a sharp knife-edge ridge that leads to the southern summit.

An easier route from Shepherd Pass might be to head for the second major lake north of Shepherd Pass (3806m) and then climb the saddle between the real summit and the southern side of Junction Peak (the other peaks). From there one still has to climb a ridge with much exposure.

Note that Junction Peak has seven peaks, two of which compete for the real summit: the true summit at the far northwestern end of the ridge. Several pictures of Junction Peak viewed from Caltech Peak are here.
Note that the unnamed 4000m peak just north of Shepherd Pass is not Junction Peak and it does not communicate with Junction Peak. Both this unnamed peak and Junction Peak border to the east on a canyon that hosts the old Junction Trail (apparently, this was the original John Muir trail). This trail, that meets the Shepherd Pass trail at the Pothole, is in terrible conditions (and not marked on most maps) but it does lead from the Pothole to Junction Pass, which lies between Junction Peak and Mt Keith.