What legal responsibilities does a salon owner have in relation to infection control and sterilization procedures?

With no infection control your clients can get sick and possibly die. Hepatitis stains thrive on nail salons. So does staphylococcus, Streptococcus, MERS, all the way up to AIDS.  The rules are dictated by public health and safety boards and these boards publish guidelines for salons and spas and it will tell you exactly what to do.  You must follow all local bylaws and standards. These do vary from location to location. This is why you need proper training and licencing. Here's a story about a salon that didn't follow the rules www.cbc.ca/amp/1.5483716. I know a couple girls contemplating a lawsuit over this.

to keep the place clean as much as possible