Seaweed farmers use various methods to cultivate it. Usually, they start seaweed off in a sheltered hatchery for 4-6 weeks. Here they provide a stable surface or rope for the seaweed spores to attach to and then move the plants underwater once the seaweed has sprouted. Once under the sea, it doesn't need much attention or resources to grow. Sometimes other creatures colonize the surface or rope. However, seaweed farmers tend to grow in the winter months to mitigate that. If they notice a nutrient deficiency in the seaweed, they will move the ropes or growing surface to a different spot in the sea. No fertilizer needed!
Seaweed grows faster than most land plants, up to a foot a day. Once out in the sea, it can mature in 6 months or less. After harvest, some purveyors sell it fresh, but most either dry or freeze it first.