The most common way to work in a wardrobe is to exchange jackets, bags, etc. with a tag/number. Hang the jackets on racks with the tags attached to it. Hand back the items when customers return with the tag. It is recommended to hang the belongings in accordance to the flow of numbers. 100, 101, 102, etc. It'll save you lots of time.
You are usually one of the first people the customers encounter and naturally the face of the establishment. It's important you greet the customers with a smile and it's also your job to make them feel welcomed and feel safe as the person guarding their stuff.
Inform a security guard or someone in charge if you believe a customer is too intoxicated. It is not your job to approach customers in these instances. The same goes for aggressive and abusive customers as well as any offensive acts.
A lost tag is very often than not something that happens. Tell the customer politely that you are not allowed to hand out belongings without the tag or a form of proof. Tell them that they either can leave their phone number and you'll later on be in touch, or that they can wait till end of night to easily locate their stuff. Do not try to solve the problem on your own if there are no tags in exchange for belongings.