Yes. Starting with the female fish with eggs, the ovigerous female--and in this case, let's say it's an Atlantic salmon on a farm--the female produces two long strings of eggs. I've forgotten how many eggs; I think maybe 900 to 1,000 per female. These eggs hatch into what's called nauplius larvae, and they go through three stages of non-feeding moults, when they shed their outer integument and grow.
The fourth stage is called the copepodid, and it is a stage that has a little filament that it can use to attach to a host. All these four stages that hatch from the eggs are carried in the currents and the plankton, and at the infective stage, which is a few days of life in which it has to attach to a fish, when it bumps into a salmon or somehow finds a salmon—and it's usually a salmonid of some sort, but it could be a stickleback or a herring—it attaches.
Then it goes through a whole series of moults while it's attached. It gets larger and larger and finally becomes an adult male or female. They mate, and more eggs are produced. The whole process, depending on temperature, takes about 45 to 50 days.