There are 3 main ways to approach Black Tooth from the north: Little Goose Trailhead, Cross Creek Lake, and Karney Lake.
Little Goose Trailhead requires a good four wheel drive vehicle with plenty of clearance. During parts of the year West Fork Little Goose Creek is too deep to cross with most vehicles, so the trailhead cannot be reached. From this approach it is about 14 miles to the base of the Penrose Cirque.
The Cross Creek Lake trail meets up with the trail from Little Goose Trailhead at close to Highland Park, but is 2-3 miles longer than the Little Goose Trail.
The Karney Lake trail is by far the shortest, Karney Lake is only about 3 miles from the base of Princess Falls. The drawback to this approach is that you need a 4 wheeler to drive the 16 miles of motorized trail to the Karney Lake.
All of these approaches converge at Princess Falls at the start of Penrose Canyon. Princess Falls are about 10 miles from Little Goose trailhead.
Cross the creek at the base of the falls and head up the right side of the falls, there will be a faint trail to follow until you reach a rock wall near the top of the falls. This part gets tricky when you are carrying a pack, you have to climb a short series of ledges and chutes to get over the ~70ft wall, it doesn't get over class 4.
After you get over the wall, start looking for cairns. For the next mile it is a bushwhack from cairn to cairn until you reach the first Sawtooth Lake. There are spots to make camp along the first 4 lakes, there are about 10 lakes total.
From camp at the first few Sawtooth Lakes it's about a 2-3 mile boulder hop to the base of the Penrose Cirque and the base of the northeast snowramp.
The snow in the ramp is usually pretty soft and not worth trying to climb in, so stay on the rocks off to the right side of the ramp. The ramp is class 3 to low class 4 until you reach ~12,600ft then the climb turns into a series of chutes and chimneys that are a low class 5. The bare part of the ramp will turn into a ridge above the snow, so try to stay on the snow side of the ridge. The crux of the climb is a 50 foot chimney that some people choose to rappel down, the chimney is low class 5 at the most. It really isn't worth bringing gear just to protect or rappel down this one spot. After you climb this chimney there is a fairly steep scree slope leading to a notch below the false summit of Black Tooth.
scree slope notch
Once you reach the notch, you are only about 20 vertical feet from the top.
Having an ice axe is a good idea if you want to descend the snowramp. The snow is pretty steep, glissading is a bad idea unless you have an axe. I skied down on my feet and zig zagged, but I almost lost it on some ice.
Gear you might want to bring: Ice Axe, crampons(depending on the amount of snow), and a light rack if you feel like packing it in 14 miles just for a few spots on the climb.