Instructions
Locate a wooden or silver plate or a large platter. You can find a wooden plate on just about any table in Skyrim, though you can also easily find silver plates and platters in any of the major cities' castles.
Enter a store and find a flat wall. It must be completely flat; if there is a support beam or window in the way, the glitch will not work. Try out the second floor of the White Phial in Whiterun, as it's a fairly easy wall to get through.
Open your inventory, locate your plate or platter and drop it as close as you can to the wall you want to try running through.
Look at the platter on the floor and press and hold the grab button. The specific button you press will depend on whether you're playing an Xbox 360, PlayStation 3 or PC.
Lift up the plate and position it against the flat wall with the bottom facing out. It can be tricky to maneuver the plate into this position. If you can't get it, try laying the plate or platter face-up on the floor. Push it against the wall and you should see its leading edge sink into the wall a bit. Drag the plate upward and the bottom edge should stay in place, allowing you to flip the plate bottom-side-out against the wall.
Sprint into the back of the plate or platter until you pass through the wall. It may take a few tries to get it right, but when it works, you'll pass right through the platter and the wall and end up on the other side.
Explore the area you find yourself in. Some walls will simply drop you off the edge of oblivion, eventually respawning you at the entrance to the building you were in. Others will land you outside the game level, allowing you to access inventory chests below shops.
Attempt this glitch on any flat surface you can find. Once you've mastered the trick, you'll be able to get around locked doors, skip through walls to avoid fights and find all sorts of strange places you were never meant to see.