Whether you want to maintain a dyed hair colour or are facing a dye emergency and want to redye your hair soon after another dye job, dying your hair once means you will probably be doing it again sometime soon. How soon depends on the type of dye you used in the first place and the damage you are willing to put your hair through.
If you just dyed your hair but are now realising that you picked the wrong hair colour or that it doesn't actually match the colour on the box, or if you are already in search of a new look, you have a few options. Since dyeing your hair is exposing it to harsh chemicals, it is recommended to wait to redye your hair. If you used a demi-permanent colour, try washing your hair a couple of times to see if the colour it fades to is more satisfying for you. If not, you should wait at least a week or two before trying to repair the damage with a new dye job.
If you used semi-permanent dye for your new colour, then the colour should last for only six to 12 washes. However, if you use shampoo and styling products that help maintain hair colour you might be able to wait longer than this before you redye. If you are planning on sticking with one colour for a while, it might be best to go with a more permanent dye to avoid re-dying so often.
Demi-permanent colour lasts between 24 and 26 shampoos so it should be least a month before you need to redye. Again, it is best to wait as long as possible for the health of your hair between dye jobs, so if you are positive about the change you want to make then it might be worth it to use permanent colour. If you are not sure, this is a good choice as it will eventually wash out.
Permanent hair colour is exactly what it sounds like: it will not wash out of your hair, so you'll have to redye every four to six weeks when you begin to notice your roots growing out. It might be worth it to invest in some colour-safe shampoo and other hair products to try to extend the colour between dye jobs as dying your hair damages the hair every time you do it.