This is the most climbed 6000 m peak in Ladakh at 6153 m (20,180 ft). The view from the top, weather permitting of course, is spectacular. While all the trekking agencies do this as a four day trek if you are already acclimatized it can be done in 2 days one night from Leh. I would highly recommend doing an acclimatization trek before then doing Stok Kangri. It is best to do a trek where you will sleep very high, close to or above 5000 m. The Markha Valley is good trek for this as you can stay at Nimaling which is 4800 m (and you don't even need your own tent) even better would be to stay for two nights there and do a high day hike during the day. Another good hike would be the Rumtse to Tso Morrri but make sure you've spent some time in Ladakh, at least 4 days, before doing that one due to the high altitude from the start . Acclimatization is critical to successfully completing this climb. Make sure you are well acclimatized and familier with the symptoms of AMS. See ismm.org for a good review of symptoms and treatment of AMS.
Do It Yourself Information
The tricky part is figuring out when to cross the glacier, walk down the left side of the glacier that descends from the mountain to the south of Stok Kangri until you see a large slope descending from the peak of Stok Kangri opposite you then cross the glacier and head up the slope. As it gets steeper make your way over to the southern ridge and follow the ridge to the summit. More than likely there will be several guided groups going up at the same time so you can always follow them if you don't feel confident.
There is a well stocked tea tent where you could buy food at the base camp, its probably best not rely on this completely but you can supplement your food and you may also be able to stay overnight in the tent if you are doing it on the ultra light.