There's three ways you can approach this climb:
One, is the West Face from the South Fork Pass. After crossing the pass you traverse north, staying close to the western flanks of the crest. Cross Potluck Pass which enters you into the Palisade Basin.
Second, is ascending Bishop Pass and then making a long traverse south (cross-country) to Palisade Basin.
Third, is from the North Fork of Big Pine Creek Trail to Palisade Glacier and ascend the North Couloir of Mount Sill. On top of the ridge, traverse to the Southeast ridge of Polemonium.
All the approaches above lead you to the Southeast Ridge, which is on top or above the Polemonium Glacier.
Once on top of the glacier, there is a deep gully to the southwest that seperates the end of the ridge from the true summit to the north.
This gully descends into the Palisade Basin. You only want to go about 75-100 feet down the gully then traverse north-east 25-35 feet to another gully. From here ascend up this gully,(class 3) east until the saddle. On top of a little saddle turn north-west and you will see the summit and the knife-like ridge for your final ascent. Class 4-5.
This is the most difficult and the greatest part of the climb. You must scramble to the knife-like ridge and then traverse up it to the summit of Polemonium, while being exposed on both sides. Great view of the U-Notch. With so much exposure a rope is recommended. Descend the same route.
A good pair of hiking boots will do for a confident climber. If not, bring climber shoes, rope and couple of slings.