Sea Event cards are usually drawn and resolved each time a player ends the Turn on a sea space. The procedure is that a different player than the one whose Turn is ending should read the first part (Story text) of the card out aloud, and then let the player make any choices required, but without revealing what outcomes the card stipulates for the different choices/tests.
Sea Events can lead to an Ongoing Story being started.
Story
The game has a set of Story cards which are numbered, and which can be triggered by other cards telling the player to locate a Story card with a specific number. This can potentially lead to another Story card being fetched, and so on, until the Story is resolved. There may be conditions connected with the advancement of a Story, and if the conditions are not met, the Story can end without being resolved.
Stories can be initated by Sea Event cards, Expedition cards and Denizen cards; those cards may trigger some Skill Test or choice, whose outcome text includes a number surrounded by pluses (like "+13+"). In such cases, locate the correspondingly numbered Story card from the Story deck, and place it under the Ongoing Story cover card without resolving it, and place the card that instructed you to fetch the new Story card in the Story area of the Ship Board for the player who caused the event to happen (usually the player whose turn it is).
The newly fetched story card will stay under the Ongoing Story cover card until an End of Act puts it back into play.