I've had this certain leopard gecko for about two months now and she was brought to me from a friend who neglected her. Her vivarium didn't allow her to shed properly and is missing some toes. She's just sheded for the first time with me. It's been about three days and there's still some patches around her eyes and various places on the body but because she has been neglected, she won't let us handle her, take it off her, etc. I'm not too sure on what to do as she is very timid and practically wild.
There may be no immediate solution, but you can train her to enjoy your company. I inherited a very old leopard gecko who didn't get enough attention. If you slowly show that you mean the lizard no harm, eventually she may come around to being handled. Start by talking to her when you feed her so that she knows your voice is the one that is taking care of her. Use that same voice when you put your hand on the cage and always let her come to you. If you ever do pick her up, make sure you hold her correctly (plenty of support under the belly and legs). It took a little over a month but our gecko lets me "pet" him. He's still uncomfortable being held, but he allows it now.
For the short term, check the link in the comment above My leopard gecko sometimes has trouble shedding. How I can I help?