The East Ridge is one of the most classic routes of Aoraki/Mt. Cook. The East Ridge joins the Summit Ridge of Mt. Cook 200-250 meters south from the Middle Peak.
The easiest way from Mt.Cook Village is to take a ski-plane to the Grand Plateau. It costs money, but saves your time and forces. Info about this service you can get here http://www.mtcookskiplanes.com/
Another option - from the Mt.Cook village approximately 20-25 km of quite good road which ends in 4 km before the Old Balls Hut - the first shelter on the route. Then follow the track which goes down from the moraine to the Tasman glacier 200 meters from the Hut. Then by the wide moraine pocket head up the Tasman glacier until its junction with Ball Glacier. Then cross the Ball glacier and by sometimes hardly visible trek by slide-rock slopes get to the base of Boys Glacier (be careful of falling stones). Climb the glacier and head up to the Boys Pass. (crevices). From Boys Pass traverse the easy snow slopes to the Cinerama Col. There is avalanche danger on this part of the route. From the Cinerama Col descent to the Grand Plateau and traverse it to the Plateau Hut (a lot of crevices!) From the Balls Shelter 10-12 hours.
There are two ways to get to the ridge: one is from Cinerama Col. From the Col descent 200 meters in the direction of the Plateau, then turn to the left and head up by the glacier to the small winding arete which joins the East Ridge below the black rocky bastion.
The same arete you can gain also by the wide snow shelf below the East Face - this variant is longer but more convenient if you use the Plateau Hut as your night shelter.
Gaining the ridge is normally not a problem. It can be complicated by deep snow and be quite long and tiring but technically easy. After gaining the Ridge follow it until the base of the Rock Bastion. Then climb two pitches of schist rocks of moderate difficulty (pitons and slings). This section can be complicated if rocks are covered by snow. After climbing the Rock Bastion just follow the Ridge (snow stakes, ice-screws)until the Summit Ridge with leads to the Middle Peak of Aoraki/Mt. Cook.
For the route itself: rope, crampones, iceaxes, helmets, 3-4 pitones, 3-4 nuts of middle size, slings, 2-4 snow stakes, 2-4 ice screws
More info on the Mt.Cook, photos, GPS coordinates you can find on the web page of Alexclimb Mountain School