If you're sailing on the Carnival spirit-class ship (Spirit, Legend or Pride), you have access to 5 launderettes available for use throughout the ship.
Locations of Self-Service Launderettes on Carnival Spirit-Class Ships:
Riviera Deck 1 - midship / across from 1219
Main Deck 4 - aft / across from 4230
Upper Deck 5 - aft / across from 5270
Empress Deck 6 - forward / across from 6102
Verandah Deck 7 - midship / across from 7267
At a bare minimum, each launderette has soap, bleach, fabric softener and laundry bag dispensers, one washing machine, two dryers, and an ironing board with iron.
The cost for each is below:
Soap/detergent costs $2 per load
Washing machine is $3.50 per cycle
Dryer is $3.50 per cycle*
Ironing is free
*Each load of laundry requires 2 dryer cycles, so it'll cost $7 per load of laundry
There's also the option of sending your laundry to the valet via your room steward however this surely will cost much more than doing it yourself (unless you're a Platinum or Diamond guest).