You shower floors are very prone to accumulating scum and moulds, since they are subjected to much moisture. If you haven't cleaned your shower floor in a while, then expect things to be a little difficult. Nevertheless you shouldn't put it off for two reasons: it wouldn't be hygienic, and cleaning it later would only make the job even harder.
You can always use soap and alcohol to try and clean all the stains and scum, but chances are good that you'll only get a little of it with this method. If you want to save time and effort, then it might be a good idea to purchase specialized cleaning materials. These are specially designed to address the kind of cleaning problems that are common to bathrooms. Also consider buying specialized equipment that will allow you to minimize physical exertion while maximizing efficiency.
Wax is a nice way to finish off your cleaning, and it will give a nice smell and sheen the shower floor. Don't use too much though, since a slippery surface is a recipe for disaster.
When it comes to shower floor cleaning, the idea is to do it regularly so that scum and other things won't accumulate. Not only will you keep your shower looking nice and clean, you will also avoid any unhygienic elements and protect your health and that of your family.