Almost all events can be done by someone who is at the level 15 quests, which most people get to in the first day. In rare cases, events require you to be at the level 50 quests, which can take days or weeks but is still nowhere near the max level quests at level 80.

The events are announced on the lodestone and you also see it on the launcher when logging into the game. The announcements link to a dedicated website for that event that gives clear information on how to get started, the requirements and the rewards.

https://na.finalfantasyxiv.com/lodestone/news/