Although MRNP no longer maintains trails past Pinnacle Saddle, as other reports note, there are basically two options up to the rocky basin on the north side of Plummer about 250 ft below the peak. One is the clear path you can see on the north side of the ridge as you're coming up Pinnacle Saddle trail and the other is just on the south side of the ridge after you reach the saddle. If there is snow, which there isn't now, the north way is fine with only a little exposure near the gully to your left (south) before you reach the rocky basin. The south way is also fine with basically no exposure. Both look deceptively more treacherous to those with fears, but they really are quite easy. The north way is probably easier to follow going up and the south way is pretty easy to follow going down because you can look down on the rocky trail and see it whereas looking up it can be hidden among the rocks.
Once at the rocky basin the tread is quite fine all the way to the summit except for a mild scramble to near the top that has tons of good solid rooty handholds and really no serious exposure. The summit is a long rock bench that provides amazing views of Rainier, the rest of the Tatoosh Range peaks, Tatoosh Lookout site, Goat Rocks and Mt Adams.