The Trading Center is quite simple. To make a Trade, you name it, you pick what to put in it - Lionesses, Adolescents, Items, money, whatever you want, as long as it is below 100 items as it is the maximum! Below, you enter what you'd like in return, and create the trade. (remember, any item or money put in trade will disappear from your inventory and/or bank to be in trade stash!)
Other players can make offers on your trade - and you can pick what you like best. Other offers will be automatically cancelled and their items/lions/beetles refunded to them! However, you can't put a pregnant or hunting lioness in a trade or offer, you can't send a lioness that recently gave birth alone otherwise, her cubs will follow, you cannot send a patrolling sub male.
You have a confirmation to make sure you choose the right things or actually want to do the trade.