The shopkeeper is a character who owns and works both as a cashier and as loss prevention at the Tool Shop of Mabe Village. It is believed that speedrunners have driven his business to bankruptcy.
Stealing from the shop requires exiting while the shopkeeper is facing up or to the right. The shopkeeper turns on a cycle of alternating 32 and 96 frame durations (so after 32 frames, he'll turn, then after 96 frames, he'll turn again, and the pattern repeats). To add to this, Link takes about a second to leave the shop. The strategy for stealing from the shop depends on what items you're stealing.
If you're stealing any of the three items to the left: * Grab the item * Walk above the shopkeeper and wait for him to turn towards you * Wait half a second, then leave the shop This strategy is the best as, if he turns after the 32 frame duration, you'll (hopefully) leave the shop before the 96 frame duration ends. If he turns after the 96 frame frame duration, then waiting half a second will mean you'll start moving on the next 96 frame duration.
There's no real strategy for getting the item above the shopkeeper on the first try as he usually turns towards you before you're able to leave.
So long as you have enough rupees to buy an item you want, items can be bought at a 100% discount if you save & quit on the same frame as you say "yes" to buying something. This can be set up by holding B and select as you enter the shop, tapping A to grab the item of interest, then holding start during the shopkeeper's prompt so that when you press A to say yes. You can finally release all those buttons after the save & quit menu comes up. Once you re-open your file, you'll find the item in your inventory, and the shopkeeper none the wiser.
This trick typically fails due to faulty inputs. Always make sure to release any directional input before the final A press to ensure the S&Q menu can come up. Info on the technicalities of the button inputs for the S&Q menu can be found in the notes section of this page