On the front-page 'Today in Battle for Azeroth' section, you will see what Emissary quests are up.

Wowhead has developed a feature that shows what quests are active in-game. There are hundreds of World Quests and only a handful will be up at a time, so there is a low chance you will see the same quests repeatedly. World Quests are the same for everyone on your realm, so you can find people easily to complete group quests. However, when you complete a quest, a new quest will not automatically spawn. There is no cap on the amount of World Quests you can complete a day. They do not 'reset' at a certain time like daily quests. World Quests all have different durations, with longer durations reserved for more challenging quests.

If you already have your Flight Master's Whistle from Legion, these quests will upgrade your whistle to work in Kul Tiras and Zandalar. This will also award the handy teleport item Flight Master's Whistle.

At level 50 after completing the unlock requirements, world quests appear in all Battle for Azeroth zones: Tiragarde Sound, Drustvar, Stormsong Valley, Zuldazar, Nazmir, Vol'dun.

Note: If you haven't picked up your Heart of Azeroth yet, you will need to complete the short questline to do so first - beginning with an Earthen Guardian (Kul Tiras) / Earthen Guardian (Zandalar). If you already have unlocked World Quests on a 50 character before, future alts can simply talk to the respective NPCs to unlock world quests, although you do want to have at least 1 outpost unlocked on the opposite faction's continent to have access to their world quests.

Track your progress in the Battle for Azeroth Attunement Tracker.

Hit Friendly with the 3 major Kul Tiras (if Alliance)/Zandalar (if Horde) factions, in the quest Uniting Kul Tiras/ Uniting Zandalar.

Unlock all three footholds as part of the Alliance or Horde War Campaigns.

World Quests in Battle for Azeroth are content designed to be an improvement over daily quests.

Do world quests count as daily quests