Maybe this is helpful. Let me know if I fukced something up.
Capturing - including using traps
The way capture works as of v0.115.0 is: you must have capture cards in your deck. It is best to make at least two card decks - one for combat (no active capture cards) and one for capture (not a big deck - if you use the whole deck the capture cards will get lost and you will be stuck for a long ugly battle). Upgrading the capture cards reduces the draws used for each card from 5 to 4 - 5 draws is more than the player gets to start with.
To use traps, set them on the ground next to your target before the capture attempt. Every trap used replaces a time you have to throw a capture card in the battle. A used trap is considered sprung and you don't get it back.
SO - you have loaded your capture deck and obtained or built some traps and placed them up top in your inventory AND cleared out a cell in the jail. You can just go try to grab whatever you fancy or better yet check the brothel and see what is in demand and fulfill one of the brothel's requests to get more rewards.
Go to where your target is, place a trap next to it (or not, it's not required) and select "try to capture" when you click on the target. You usually need to throw the capture card five times or more (there is a counter on the right-hand side of the screen) and then one last time at the end. The captured mob goes into your jail cell. The food cart at the jail door is for feeding your captive(s). Berries and some other stuff you might have grabbed up can be used, or go to Herbalica and buy bread and cheese.
Train your captive in the skills the brothel is looking for and leave it at that. I like to do the card game up to level five. At this point you have to complete a five-card sequence to advance so I just back out and do the interactive thing from level five up. If you train each mob right away and send it to the brothel you won't have to buy jail cells and you will save on buying food.
You can also get capture quests from Mirana in the tavern. You don't have to use up your jail cell(s) or food or spend time training them and the pay is good.