What do I do with the cage, I put someone isnide of it and put berries, but nothing happens
Raping a girl, whether asleep or awake will knock them out just like when you use a club on them. Any knocked out characters can be picked up and put into cages. Any NPC that can be tamed can be placed with their preferred food, which can be checked in your inventory, into the cage together, and after a lengthy period of time, they will be tamed.
Tamed characters can be assigned tasks around a location you can set, or can accompany you on your travels. They'll teleport to you if you get to far away while traveling together. You can only have a limited amount of allies accompany you at a time, but they'll help you fight and can't die. They can be knocked out, but will get up again after a little while.
If someone is traveling with you, they'll build up affection for you as time passes. If an animation exists for it, characters who like you will engage in consensual sex with you upon request. This applies to both Yona and the Male Protagonist.
All NPCs have personalities that they like and dislike. If two NPCs with the relevant animations have enough affection for each other, they'll engage in sex on their own if there's a bed nearby.
Alternatively NPCs who hate each other enough will start fights or rape one another, so make sure NPCs with clashing personalities are kept separate. Tamed animals will run wild and must be knocked out to interact with them again.