To begin, set your gender by doing /marry gender (gender).

To send a marriage request, do /marry [username]. When you are married to another player there will be a little heart next to your name in chat.
 

When you're married, you will have access to the different marriage features. If you want to give an item to your partner, simply do /marry gift with the item in hand. You can "kiss" your partner by shift right-clicking on them. This will cause particles to displayed around both of you with a sound effect. If your marriage partner and you are 5 or less blocks away from each other, then you will have 2x faster health regeneration. You can also heal your partner by doing /marry heal. This will take health from yourself and transfer it to your partner, but you will not be able to go below half a heart of health. As a married couple, you can have a shared home. Either partner can modify this home location at any time. Do /marry sethome to set a home location, and do /marry home to teleport to it. You can instant teleport to your partner at any given time with /marry tp.
 

Divorce your partner by doing /marry divorce. If you divorce your partner, then you will have a 1 day cooldown before you can marry someone again.