The North Ridge is a fairly popular route up to the summit of the Middle Teton. It offers a relatively easy but exposed route to the summit from the lower saddle, thereby lending itself to climbers as the route of choice while traversing from the Grand to the Middle.
The inside of the famous "black dike" looks like a long hallway. Once you're here, you're only a few minutes from the summit.
Once at the lower saddle, climb south (left) toward the base of the north ridge. This is just easy scrambling. The first real features you will come to are two small pinnacles, Pinocchio Pinnacle is the first one, and Bonney's is the second. Go right (west) of the first and left (east) of the second to negotiate this area. There is an easy class 4-5 move to gain access to the notch formed between the two pinnacles. On the east side of Bonney's, there is a slabby section that angles toward some exposure above the Middle Teton glacier. Hug the right side of this slab and make your way south to the notch formed by the first small black dike. Descend into this notch and climb up the obvious series of ledges (50-60 feet) leading up and left, then right around the base of the north ridge. Some exposure is experienced here. Make your way around the ridge line to the right until you can see into the northwest ice couloir. Work your way up on a series of ledges and features, staying quite a distance below the true ridge line, but also significantly above the ice couloir. Eventually you will encounter the large black dike that is the prominent feature on the Middle Teton. At this point on the mountain, it resembles a large hallway.
The obvious wedge shaped cavity is the crux if one wishes to do technical climbing to reach the summit. The bypass is reached by maneuvering to the right along the top of the pinkish boulders in the bottom right of the photo.
Continue up this feature until you're near the top. On the right side of the dike, there will be a series of ledges and features leading up to a large wedge-shaped cavity on the south side of the dike. It is easy scrambling to the base of this area. Here is the crux of the climb. There is a harder system of cracks on the right side of this area, (5.7-8) or an easier, shorter system on the left side (5.6). If one wishes to bypass this portion to avoid technical climbing, there is an alternate route located maybe 100 feet or so to the west. Starting from the area where the crux came into view, climb up a few feet and cut right and around the base of the rounded feature that is situated to the right of the crux. There is a system of slabs that lead around this to the right. This route does not involve any climbing, but it does present more exposure and requires an awkward step-around move, so it may not necessarily be the lesser of the two evils, so to speak. It all depends on experience. Either way, once this section is behind you, it's nothing but easy ledges to the summit.
Necessary gear is always situationally dependent. Required equipment depends heavily upon the experience of the climber considering this route. For one who is experienced and comfortable with exposure, this route can be soloed fairly easily. If a climber wanted to use protection, maybe 3 or 4 small to medium sized cams or nuts should do the trick. However, it's always better to have it and not need it, than need it and not have it. No more than 60 feet of rope would be necessary for any point on this route. There are a couple places where sticky rubber or approach shoes would be helpful, but certainly not required if one is mindful of their foot placement.
No permits are required for any of the major peaks in the Tetons, but for those wishing to camp overnight, a permit must be obtained from the Jenny Lake ranger station. It's located only a few minutes north of the turn off for the Lupine Meadows trailhead.