Q: How do I set the indigo dye?
A: Quick answer : Air and something acidic.
Long answer : Indigo is a vat dye. The pigment molecules adhere to the fabric when they are in an elevated pH and chemically reduced (devoid of oxygen molecules in this case). When the fabric is reintroduced to the chemicals in our atmosphere (namely the oxygen in air) it oxidizes, turning from leuco-indigo to indigotin by incorporating oxygen. The when entirely blue, the piece then needs to be rinsed of all excess pigment and submerged in an acidic bath. The Indigo & Shibori Natural Dye Kit includes a packet of citric acid which can be used to create a rinsing bath for your work. Citric acid in water is historically called a "Sour Bath." This sour bath will bring the pH of your goods down from the pH11+ conditions of the indigo vat. Many other acids can be used including vinegar, lemon juice (essentially liquid citric acid), or strongly steeped black tea.
For longevity of your dyed goods, a soy post-treatment can help to protect from wear and UV exposure, see the answer to this question for more information.