You need to already be pursuing a relationship with Sera, and have relocated to Skyhold after the first series of repairs.
Assuming Sera's disposition is high enough, this quest will trigger when you speak to her again after saying that you are interested in her. She will tell you that she bought you a hat; the Inquisitor is concerned that she needs to get Sera a gift in return. To complete the quest you need to speak to each of the companions (in any order).
The companions express surprise upon learning of Sera and the Inquisitor's relationship, some positive (Varric, Blackwall, Iron Bull) and some negative (Solas, Vivienne). Most of them have no idea what would please Sera. Iron Bull, Solas and Blackwall offer no ideas. Cole recommends not giving her a gift in the Fade, Varric tells the Inquisitor to avoid subtext or words of any sort, Dorian makes up a story about the "Lover's red", Cassandra's only suggestion is that Sera gain purpose or an actual profession. Vivienne sarcastically remarks that the Inquisitor should just shave her pubic hair to say something crude. If you agree to do it an exclusive cut scene with Sera will trigger.
Once you've talked to all the companions, return to Sera. The Inquisitor will take Sera to her quarters, and tell her that she's been worried about finding the perfect gift for her. Upon learning that the Inquisitor told everyone that they were in a relationship, Sera exclaims that this was the best possible gift and takes the Inquisitor to bed.
If the Inquisitor did as Vivienne suggested, Sera will laugh when she sees what the Inquisitor did and fall off the bed. She'll then pull the Inquisitor down to the ground with her.
Officially in a relationship with Sera.