This page of the guide to Greedfall contains information on how to start a romance with Siora. To romance her, you must first complete side missions entrusted by this companion: Find Queen Bladnid, Promises Set in Stone, and The Queen's Farewell.
The right answers in conversations with Siora:
How did you know the missionaries were lying?: Tell her that it is logical, given their culture. +2 reputation with Siora
What is she going to do now?:Tell her that you would understand is she had to help her people. +2 reputation with Siora
Romancing Siora in GreedFall
If you completed the side missions and you chose the right dialog options, Siora will offer you a meeting during your next conversation. Agree and visit any of the residences - go upstairs, and Siora will ask you to spend the night together. The next morning, the woman will confess her love - you can say the same to her.