Best way, gets out any stains, i do it once a month for all my tzitzis, and leaves them white (this is for wool)
Take a bucket, put in the tzitzis, put in a spoon of oxi clean, add warm water (enough to cover tztizis).
Then mix the water and agitate the tzitzis for about a minute, and let them sit for 15 minutes. If you let them sit for longer then 20 the black will start to bleed. Then agitate them for another minute, take them out and wash under cold water. Hang them up to dry and here you go. If you want you can also iron them