While the East Face deserves its classic status as the first technical route on the face, the East Buttress is arguably the better route. It is more sustained and aesthetic. It is also less crowded and has less loose rock.
The difficulty rating is variously given as "Class 5" (Roper), 5.6 (Secor), 5.7 (Supertopo), or 5.8 (Moynier & Fiddler). The rating depends in part on who you ask, and which specific variation (they are legion) you are talking about. The route description provided here roughly follows the line described by Moynier & Fiddler. They refer to this line as the "direct route", as will I.
The crux moves are located in the lower part of the dihedral on the second pitch. Given the subjectivity of ratings it seems silly to argue over the "correct" rating. Personally, I didn't feel it deserved a 5.8, but that's just one opinion. The remainder of the route is quite a bit easier.
With the exception of the crux moves (wouldn't you know it?) the route protects very well. If 5.8 is near your upper limit, and your style is to place a lot of gear when the going gets hard, you'll probably find the shallow, flaring cracks around the crux disappointing. Fortunately, it's a short stretch. There are some opportunities for solid, small nuts just below, and the pro gets much better just above. You can always opt for the FA route and enjoy the remainder of the climb free of cold sweats and hyperventilation.
The standard approach is the same as for the Mountaineer's Route. Begin on the main trail from Whitney Portal, pass one stream, and then turn right just before the second stream crossing (signed). Follow the use trail up to a willow-choked valley. Halfway up the valley the trail crosses back to the north side of the stream and runs a short distance along the base of the cliffs.
Scramble up a short class three gully to a series of ledges (the Ebersbacher Ledges) that lead east to a point where it is possible to step up and head back west on tree-covered ledges. Continue up to Lower Boyscout Lake, take the use trail on the south side of the lake through talus to a point where it is possible to pass through the willows onto slabs. Head up the slabs to Upper Boyscout Lake. Head south from the outlet of Upper Boyscout Lake and pick up the use trail again, and follow it until reaching a gully system (marked high on the right by a water seep) that leads to Iceberg Lake.
The final thousand feet of the approach ascends talus and then third class terrain to the right of a prominent buttress above Iceberg Lake. Follow this to a notch behind a tower. Rope up here. Note that this is not the same chute as the Mountaineer's Route, which is the big gully to the right.
A more detailed description of the approach to Iceberg Lake can be found on the Mountaineer's Route page.
The start of the East Buttress as seen from the notch where both the East Buttress and East Face begin.
The direct route ascends two pitches to the top of the obvious tower looming above the notch to the north. Follow broken ground (up to 5.6) to an obvious left facing corner (5.7 or 5.8) leading to a belay on the top of the tower. About halfway up there is an inobvious belay ledge off to the right. Finding this is preferable to setting up a hanging belay low in the corner. If the steep corner above has you sketched out, you can traverse right around the tower and then up allegedly fourth class terrain to the top of the tower. This is the first ascent route.
Begin the third pitch by traversing the top of the tower and dropping into a notch. From here you have two options: either climb the short face/arete just to your left (up to 5.7, less than stellar pro) or drop down to the right over a big step (awkward if you are not real tall) to a ramp (up to 5.6). Both options converge on a belay on a large, sandy ledge at the base of a prominent right-facing corner/flake system.
Looking down from the top of pitch four. The prow of the buttress is the sun/shade line in the lower center of the picture. Above this we see the tops of two towers. The route ascends the left-hand one. The "poorly protected" third pitch climbs the brighly lit section just left of the shaded prow. The third pitch ends at the big sandy ledge in deep shadow. The fourth pitch ascends the corner above that.
Loooking up the upper half of the East Buttress. The "PeeWee" is plainly visible. The route passes right of the "PeeWee", then goes up and slightly left above it, though there are an infinite number of variations.
From the top of the "PeeWee" climb a face to a right facing corner (5.7) near the top of the buttress. Once above the corner, about 300 feet of third-fourth class climbing leads over and around blocks to the summit. While it is possible to continue roped climbing by staying as close as possible to the now-indistinct arete, this hardly seems worth the effort.
The upper buttress is such a jumble of blocks, talus, and towers as to defy description. At this point, many parties are ready to call it a day and get on with the descent. However, if you are going to have an epic on the East Buttress, this part of the climb presents many opportunities. In general, staying to the left will lead you towards the upper part of the east face, and the easiest way (a short stretch of south-facing class four) past the final steep section. If you hit it right you will top out within feet of the summit, and perhaps a few gawking hikers who never considered the possibility that the face could be climbed. Then again, there are also 5.10+ finishes where your huffing and cursing may prompt well-meaning walkers to pull out the cell phones and call Inyo County SAR.
Descend the Mountaineers Route to Iceberg Lake.