You are only able to get married after you have completed the main storyline. In order to get married, you first need to buy the house expansion and an upstairs. Then, you will need a large double bed. You can buy this from James at his shop in the Church Plaza on Thursdays or Holidays for 8,000 G.
After the expansions are purchased and the main storyline is beaten, all that is left is to finish wooing your chosen bachelor or bachelorette to 10 LP. After you have done so, you must first ask that person on a date - which will be two weeks after the day you ask. After the first date, you will receive a request from Gerard about needing materials. Once you get what he needs, you will receive the Engagement Ring to propose to your sweetheart on the second (or whichever) date.
If you walk away from your date before proposing, the date will end and you will have to wait for yet another date.
For Sonja, be sure to speak with your date after it's finished and ask them why they're fidgeting so they can ask you to marry them.