Well a few things....If you are serious about Graphic Design you need to have a Portfolio of work. No one will hire you without it!
Second you need a way to market yourself. This can be done in many ways. Flyers, Cards, Newpaper ads, ect.
2) Big way to get a start:
A) Go sell yourself to small business owners. Dress to impress and walk into many small stores in your area. Ask to talk to the owner and go for it! Have prices ready, examples of Logos, Flyers, Ads, ect. right there to show them. Give them a card and tell them no pressure just call you if they need anything done!
B) You should also As a developer....HAVE A WEB SITE!!! Make it an online portfolio! Have ways on how to contact you on it and make sure it looks good. Don't have a cheesy mostly text web site when your trying to be a web designer/graphic designer.
Get business cards and leave them everywhere!!!! any bullitin boards you can, pass them out durring conversations, ect. Make sure there are multiple ways yo contact you on it.
Hope this helps a bit.