It is okay to wash your newly dyed shirt as you would your normal clothes. However, make certain that you wash it completely separate from any other clothing to avoid dying other items accidentally, and only after you've rinsed the excess dye from the fabric. The Dharma Trading Company suggests using pH neutral professional textile detergents, such as Synthropol, for optimal results.
Tie-dyed items must be washed prior to wearing. This prevents the colors from running and keeps leftover dye from staining your skin and other clothing. Following the dying process, run the still-bound garment under cold water to cease the dye's reaction with the fabric. Then, while you remove the ties from the garment, run warm water over it to rinse away any remaining dye. Lukewarm water will suffice.
Run the warm water over the garment until it wrings clear or almost clear. (It goes without saying that the rinse stage of tie-dying should take place in a sink or tub that is a safe distance from anything that you'd care to not get dye on.) It is now safe to wash as normal. After the first wash, your tie-dyed shirt is ready to wear and can be washed with your regular laundry.