I did not paint crochet thread. I paint a floss. I prefer natural dyes: tea, coffee, berries, herbs. Threads can be dyed by immersion in a color solution or boiled in a "brine". If you're interested, write a comment I'll try to explain.
I've dyed a bit of cotton. It's much more difficult than wool. You need to use a dye for cellulose fibres like Procion mx and the fixative is aLOT of salt and a pool chemical. If you are serious about it google is your friend. A more approachable dye is the sachets (eg dylon) that you can get at the supermarket. Those have clear instructions on the package and that method is much less expensive. To make sure your dyed yarn has uneven colour don't agitate it as much and put part of the skein into the bath earlier than the rest.