Instructions
Go to the Eagle Inn and talk with Cecilia every day of the week. Speaking with her daily raises her love interest points slightly each time.
Give Cecilia a gift she likes daily. Cecilia enjoys receiving gems, which can be found while mining. Use a charged Battle Hammer while mining on Blessia Island if you need to stock up on gems. Only give her one per day. The first gift of the day raises love interest points, but successive gifts that day do nothing.
Buy an Aquamarine Brooch from Yue, the shopkeeper, and give it to Cecilia on the 12th day of summer. This is Cecilia's desired birthday present.
Visit the Bulletin Board in town and look for Cecilia's quests. You must do all ten quests she issues if you want to marry her. Her final two quests are directly related to marrying her. In the ninth, you receive her proposal gift. In the tenth, you need to marry her to finish the quest.
Take Cecilia with you to all festivals whenever they occur. Festivals give her love interest points a large boost.
Go to the Messhina Valley when Cecilia issues her tenth quest. Cecilia is waiting for you there. Hand her the Round Stone you collected from completing the ninth quest.
Reply "Yeah" when asked if you like strange girls. You are then given the option to marry her.