To chiffonade basil (or anything else) you simply place a few leaves of basil one atop each other, stacking them up neatly.
Roll up the little stack of leaves into a tight cylinder — you can roll it up from side-to-side, or from top to bottom, your choice. Top to bottom will yield longer strips, in the case of basil or any leaf that is taller than it is wide. Side-to-side will give you shorter skinny strips.
Hold the cylinder and use a sharp knife to cut thin slices. Hold the cylinder with your non-cutting hand and use a sharp knife (a dull knife will crush and bruise the basil or lettuce) to cut very thin slices of the cylinder crosswise.
As you slice the cylinder, the cut slivers will start to unfurl. When you are done cutting, use your finger to gently pull apart and fluff the little pile of chiffonaded basil.
Notes
Make sure that you use the sharpest knife in your arsenal because a dull knife will crush and bruise the leaves that you’re working with.
It’s a good idea to try and hold the basil still with your fingernails and curl your fingers away from the knife as you cut to avoid nicking your fingertips since you are cutting super thin slices, and the cylinder will be pretty small.