The internet has a lot to offer budding photographers; it provides a broad platform for your work which could not even be envisaged a decade ago.
A good tool for turning your hobby into a business is by using Facebook.
This is a very cost effective way to market yourself or your business, it will take a bit of time to set it all up but you will have full control over what is shown and there will be not set up fees at the end. Always try to reflect your personality and do not make it too safe and boring.
Make it easy for potential clients to browse through your work by adding photo albums to your different pages of profile. Choose only your best work, if you have a valued blurry shot of someone famous keep it for personal use. Clients will be attracted to well balanced shots and those that introduce a bit of magic.
Ensure that you are viewed as a photographer, using specific graphics and even a picture with you actually holding camera, obvious but marketing often has to be like that. Make subject matter different from the norm; make sure you stand out from the crowd but in a good way.
Update your Facebook page on a very regular basis; it will give people a reason for constantly checking in on your work. This is all part of making a name for yourself, which after all is just what you need to happen.