There are two starting points for the direct East Ridge, both of which start low down in the Owen's Valley. The easiest starting point is the Red Lake Trailhead, located at the base of Split Mt. I will not describe that route, being that I have never successfully driven it. Tinemaha Creek Rd and McMurray Meadows Rd are both rough and require a 4x4 with high clearance. From the Red Lake Trailhead follow a use trail that heads Southwest up the North side of the East ridge of Cardinal Mtn.
The other starting point is the Taboose Pass Trailhead. For this trailhead turn west off 395 on Taboose Pass Rd, North of Independence. Follow this road west, staying right at the two major unmarked intersections. The road gets progressively worse, though is passible with a low clearance 2wd(I did it in an Acura Integra). The road deadends on the North side of the Creek at the signed Taboose Pass Trailhead. From here hike up the Taboose Pass Trail for 3/4-1mile to the base of the East Ridge.
The East Ridge starts out very broad, just continue to climb, making your way through the brush and around boulder fields. The lower section to Stacker Flat is completely open to interpretation and from the Taboose Pass TH there is no one way. Once you have reached Stacker Flat continue up the ridge, climbing toward the right(North) side of the ridge. The ridge then levels off around 9500ft and you have a couple options. One can climb directly along the North side of the ridgeline, or traverse into the valley that makes up the middle of the ridge. During winter conditions the ridgeline is the perferred route, during summer conditions much scree and loose rock would dominate the route.
Once you have reached the high plateau at 11300ft a broad bowl opens up in front of you. Choose which ever route up seems best considering the current conditions. I stayed to the left of the bowl, traversing across at the top. At the top of this bowl the ridge narrows, and you have a 12900ft false summit to ascend strait up on loose rock. After dropping back down 30-40ft you reach the final chute that brings one onto the summit ridge. In winter conditions this consists of a short 50ft 40 degree chute just off the sheer North face. In summer conditions one can scramble directly along the rocky ridge, or enter any of the loose class 2 chutes to the climbers left. Route finding is very easy and obvious, and exposure is minimal. From here scramble up past one more false summit toward the reddish brown summit block, with its evident pile of rocks and register. Views are spectacular from the summit on a clear day. The sheer North face drops off below you on side, while the more gentle South slope leads down to Taboose Pass. For the descent one can either slide down the South Chutes back to Taboose Pass, and down the trail, or follow the route whench you came back down the East Ridge.
During summer months no special gear is needed. A sturdy pair of scrambling shoes, and over night gear if you plan on staying on the ridge. For winter climbs; crampons, ice axe, and snowshoes are all recommended. In addition all other winter camping gear and clothing, plan appropriately for weather and high winds on the ridge.