The problem of marine fouling became more acute during the transition between wooden to iron ships. As the OP mentioned, copper plates had become a norm for anti-fouling by the start of the nineteenth century. Affixing such copper plates to an iron hull was problematic in that if seawater seeped between the plate and the hull, it had a strong corrosive effect on the hull sometimes mimicking a battery. The eventual solution to this problem was the development of copper oxide paints which shipyards could apply directly to the hull. Note this still does not prevent marine organisms from making a home on the ship, it just arrests their growth. Periodic cleaning of the hull is still part modern ship maintenance.

If you're interested, one of the best introductory works about the transition from wood to iron is John Beeler's Birth of the Battleship which details a number of the unexpected problems transitioning to new technology posed for naval designers.

Copper sheeting works in two ways. First, copper and its corrosion products are toxic to sea life. Second, as the copper corrodes it will separate and fall off, taking the more hardy weeds and critters with it. Copper cannot be used to cover the hull of a steel or iron ship. The copper has a corrosive ionic reaction with the iron.

Instead iron hulled ships must be covered with paint that contains chemicals toxic to sea life. This kills off barnacles and weeds that would otherwise adhere to the hull. Copper is still commonly used as an active ingredient, but the reduced metal to metal contact keeps hull corrosion low.

Steel hulled ships were also fitted with "sacrificial anodes", large ingots of zinc to minimise galvanic action of sea water on steel accelerating rusting. "Self-polishing" copper or lead based paint, often referred to as "boot topping" or more technically as "anti-fouling" was applied to minimise marine flora and fauna growth. This, in recent years, has been replaced by far more complex polymer based paints which don't cause as much collateral damage to the marine environment. Here is an example http://www.international-marine.com/antifoulings/self-polishing-antifoulings.aspx