What we know about marriage: Player marriages will involve a contract. They can take place between any, and any number of, willing parties. If there is NPC marriage (SBS appears to have changed their minds on this a few times so far), it will likely involve a certain amount of wooing, then signing a contract. Contracts between NPC's and players must be offered by the NPC, since player-player contracts can be more complex, and it would be too easy for players to cheat NPC's.
What we know about having children: Whoever will be caring for the child must have a room and some starting items for the child. A man and woman sign a child contract. Neither can have more than one child per in-game year. The child will randomly inherit a set of genes from each parent. The player who will be caring for the child will choose which genes are dominant/recessive (I believe there will be the option for one reroll of the inherited genes). Some genes might be linked into groups where your choice is between one group or the other. I've heard that the child will show up as an eight-year-old one week after the contract is signed, but I can't remember where that information came from.