Firstly, one must grasp that there are two types of courting: Courtly Love, which is meaningless and is only a way of passing the time and Sincere Courtship, which actually isn't sincere at all, because the person doing the courting probably just wants to advance themselves up the social ladder.
Courtly Love:
Writing sonnets, singing songs, flirting constantly... this is courtly love and is a constant part of everyday life in SC. Courtiers often take lovers, which is no secret, though it can become a very scandalous affair, considering adultery is treason. Also, if a young lady is unmarried, it is essential that she retain her innocence, otherwise she is a ruined woman. Therefore, families will marry their daughters to promising young men before trying to get her in the bed of a king (or a high ranking nobleman). Or, if a king has taken a liking to her, he will sometimes push for her marriage, so that she can then become his mistress.
This is all courtly love and is taken very lightly by the courtiers. It gives them something to gossip about and something to pass their time. Nothing serious usually comes out of courtly love, except maybe a few children, who, in the case they are the king's, are openly flaunted as bastards, or, if a lady had perhaps taken a lover underneath her husband's nose, the child would be passed off as her husband's, not her lover's.
Courtiers may take as many lovers as they wish. Just, if you are female, try not to get caught :). And usually, courtiers only take lovers if they feel it will benefit them in some way.
Sincere Courtship:
Most marriages are arranged by the families in question and will be if you belong to one of the top families of SC. However, if you are just an average Joe (or Jill) trying to make their way in the court, you can either arrange your own marriage, or have the head of your duchy help you out. If you see someone you fancy, drop them a line by PM and they will make sure they are available (their families don't have other plans) and then they will subtly try to bring you two together and make you more desirable to them through gifts, favors, ranks, etc.
In this world, an engagement is binding, as binding as if they were already married. It can not be broken, unless the engagement has seriously irritated a higher-up, and then... well, anything is possible if you have the money. An engagement must be overseen by two witnesses. But maybe we should talk about how you get to the engagement?
So, male courtiers, you see a lady you like. You find out all about her through your friends and mutual acquaintances. Finally, you decide to approach her. You introduce yourself, compliment her a little, and then leave while trying to keep all invitations of later meetings open. If she, and her family, is interested, then you're set. However, if her family has deemed you unworthy, you might need help from a higher-up.
Courting is a slow and steady process filled with gifts and subtle suggestions. Masques, balls, and other special events are a great time to woo the girl (or girls) of your choice without the normal pressures of court. Remember, everyone is watching.
When you finally feel your affections are known and the family is already aware of your intentions, go and buy a ring and then pop the question. However, you can not actually give her the ring until the proper engagement ceremony, though feel free to flash it to her and tell her specifically of your intentions. Then, arrange for two people - either members of her family, your family, whatever - to be present when you present her with the ring. Slip it on her finger and there you have it! You're as good as married. However, no consummation just yet :). First you have to do the ceremony.
If you have no family, the head of your duchy will help you pay for it. If you are one of their favorites, they'll probably arrange everything! If you have a family, however, they will usually cover the expenses. There will be celebrations and all sorts of fun things - the size of the celebration will depend on your rank in the court.
Please note that there are two types of engagement: de futuro and de facto. De futuro is like a promise to be married, not an actual engagement. It can be broken and is not binding. A de facto engagement is as good as being married and can not be broken unless you've seriously peeved someone very high up on the food chain.