Home Lies Over the Ocean is a Genshin Impact world quest that can be taken after completing Ritou Escape Plan (the early Inazuma quest where Thoma challenges you to find a way off the island).
You can easily start Home Lies Over the Ocean by visiting Liyue Harbor and speaking with Atsuko, the Inazuma native who once described the region's state of affairs. You can find Atsuko wandering the docks in Liyue, right next to the water and merchant stalls.
Atsuko explains her determination in making a living in Liyue, and asks for your help in delivering a letter to her parents to share that goal.
The location of her parents, Yoh and Michiru, are added to your map. Speak with them in Inazuma and learn that they believe Atsuko is already home—despite the fact that this contradicts the information Atsuko shared with you in Liyue.
Atsuko's parents ask that you come back the following night. Turn your clock to somewhere between 18:00 - 06:00 and return to the house, where you'll overhear an interesting conversation about a rescued Tanuki.
When the family comes out to meet you, you'll experience a strange encounter with "Atsuko." After she storms off, her parents suggest you return the following day. Turn your clock ahead a full 24 hours.
When you return, Yoh and Michiru explain that "Atsuko" has mysteriously vanished, leaving behind only a pile of leaves. The quest automatically concludes after this revelation, leaving the situation... resolved? Oh, well. At least you get some rewards!