No, Google my business doesn’t cost any money. It’s free, all you need is a Google account. There’s a “sponsored” version, i.e. under Google advertising, which allows you to display a 4th listing in Google search results. This specific search is an ad and is part of Google’s advertising network. Otherwise, everything else is free of charge, and is just a simple configuration and engagement method, which you can give to your customers to leave positive reviews.