The majority of your tie dye can be washed as normal with the rest of your laundry on a 30 degree or colder wash. Wash with similar colours if you want to avoid the lighter colours like yellow from dulling.
There are a couple of exceptions to this. I advise that any garments dyed in the Peacock Jellyfish or Nebula design, or any clothes that have been dyed heavily with navy blue to be washed by themselves for the first few washes. These styles often release a bit of colour after dyeing, much like you would see with a pair of indigo jeans. After the first few washes they will be fine to wash with your dark washing.
Clothing that has hand painted stars on should only be ironed inside out with a cool iron.
Clothing with a vinyl logo on should be ironed inside out with a medium heat iron.