Stack the basil leaves on top of each other, face-down (so they're curled up), with the largest leaves on the bottom and the smallest leaves on top.
Roll the leaves tightly starting on the long side of the stack. Hold the roll together firmly with your non-dominant hand.
Using your best knife (I recommend a high quality chef's knife), start slicing the roll of basil very thinly- no thicker than 1/8 of an inch. Be careful when you get to the end where you're holding it! I recommend using the bottom of the knife- the part that's closest to the handle- since you'll have more control of it
Use your fingers to separate the ribbons of basil that have formed by slicing the roll. Use the chiffonade of basil to garnish pasta, pizza, caprese salad, or use as an ingredient in any recipe that requires chopped fresh basil.
You can use the chiffonade technique to cut other broad-leaf herbs, like mint and sage, or leafy greens, like spinach. It is not well-suited to smaller herbs, like parsley or cilantro.