Who may enter a love relationship with Cassandra? You can romance with Cassandra only if you play as a male, regardless of your race. If you play as a female, you will only be able to flirt with Cassandra without any serious effects to relations with this character (after several attempts, Cassandra decides that she is not interested and suggests that you remain friends).
How to build positive relations with Cassandra? During all of the conversations participated by Cassandra (regardless of whether you talk eye-to eye, or with more characters ), pick the dialogue options that suggest your support of the Chantry. Apart from that, pick the dialogue options that convince others you believe in being the Herald of Andraste (the savior). Also, remember to pick all of the dialogue options marked with the heart symbol.
More important steps:
- You need to continue on building positive relations with Cassandra and complete two quests connected with her (ones from the Inner Circle), i.e. "Unfinished Business" and Guilty Pleasures, for which you are going to need Varric's help. Definitely, the most important one is the Promise of Destruction. Complete the quest as soon as possible. After you complete the "Promise of Destruction" quest, meet with Cassandra again. If your relationship with her is well-developed, she should suggest that you meet somewhere secluded. It is important that you stress your interest in her, during that meeting, or you will lose your chances of entering a relationship with her for good. Your next step is to get three items, during The Ideal Romance side quest. The first one is a tome of poetry that you can obtain from the book trader in Redcliffe in Hinterlands. The remaining two are flowers and candles, which you can buy from one of the traders in Val Royeaux.
- After you obtain the items, talk to Cassandra again at the Skyhold, so you can suggest a meeting in a romantic spot and use the items that you purchased.
- After a night with Cassandra, you start another conversation. Again, you need to express your being interested in a stable relationship with her (this renders romances with other characters impossible).