Follow the recognised trail to Chhukhung - the last habitation in the valley. See the map on the main Imja Tse Page for the route to the base camp.
Basically you climb steeply from Chhukhung (4700m) to the south before following the latteral morraine east along the 'true left' bank of the glacier. Follow it to the snub of the
imja glacier and walk up the narrow flat area between the morraine and the mountain. You will come to the obvious base camp where patches have been cleared for tent spaces.
You could make it to the top and back in one day, however I chose to take two to be more comfortable, to have a better chance of success, and to enjoy a himalayan high camp.
To the high camp: move SE along the base of the mountain and turn NE to climb up the steep slopes which are covered in grass and rocks at this point. There is a path at this stage. You will come to a re-entrant between two ridges and there are various places along here to put your high camp. Again flat areas have been made by previous parties on the rocky slope for tents.
From the High Camp: cross over to the right hand ridge and climb up it to gain the glacier. At this stage a guide is useful to guide one through the cravasses: not just for safety, but if you do not know the way it will take you hours to reach the summit ridge. The summit ridge is spectacular and 'airy'! It is very steep to gain the ridge and some groups have put a fixed rope up here: we didn't need to as there were only three of us, the snow conditions were great, and we were confidant enough on steep snow. Reading other people's posts I gather that some years the wall is very icy.
Sometimes the snow is very soft which makes the last pitch on the ridge itself almost impossible - we were up to our thighs and at one stage it looked as if we wouldn't make it. There is also a cravasse/ gap which apparently sometimes makes the last bit impossible.
Ice axe, crampons (though you may not need them if the snow is soft) gaiters.
Temperature can change rapidly. It is, at times, possible to summit in just a shirt, but at 6100m prepare for the chance that it could be very cold and windy indeed.
Additional Information from Clarity:
From Chhukhung to Island Peak Base Camp was around three and a half hours. From Base Camp up to our high camp was an hour and twenty minutes. We summited in six and a half hours; descent was done in about two.