Screenshot via MiYoHo YouTube
For the Where the Light Wanes Lantern Rite Tale, Hongyu, a guard in Liyue, will ask you to collect some Xiao lanterns that have drifted off. It is his job, but like everyone else in Liyue right now, he is just too busy to do it.
Lantern Rite Tales will reward you with Festive Fever that will increase the overall Fever level of the Lantern Rite event, unlocking new activities and rewards.
All the waypoints will be marked on the map one by one as you collect them. The first lantern can be found near Mt. Tianheng. It is trapped in a large root, although it is easier to climb the cliff behind the root to get to the lantern. When you reach the lantern, you can jump across to the root to collect it.