If your dye came in a kit, maybe there's a website describing care and feeding of tie-dyed articles. If not, check the package to see if it says anything about vinegar. If there's no ban on vinegar, soak your dyed items in a bucket of water with a cup or two (depending on the size of the bucket) of vinegar stirred in. Stir in the vinegar before adding clothes, of course. Vinegar helps set many types of dyes.
After a good long soak in the vinegar, wash your items in the washing machine with a very little gentle soap (like Woollite or the generic version thereof) and the coldest water the machine will run. Always wash them in cold to keep your colors brilliant, but after the first 2-3 washings you can use normal detergent.