Hello Shaun,
If you are in the graphic design game eventually when it picks up, you will advertise yourself on the work, flyers etc you will do!
To get started I can only suggest that you email (however keep it simple and not spam full i.e saying you are the best thing since sliced bread) - just point out that you are here to the company you email , your contact details and if they ever wanted to use your services then to keep you on record/in mind.
What companies you contact is up to you. It's B2B sales really. What do you provide that the other business can gain from? Do you do printing? Who needs printing? Do you do wedding invitations? Pop a few in some local wedding shops - and while you there ask if they need any work doing!
Not to drop a bomb on you, however it's a hard game to get into, when quite a few do it - including a friend of mine, so I wish you the best of luck and if I can help just PM me.
My business unfortunately is currently relying on people coming to me, and I can only promote myself to them at this current time, it's 50/50 and with my hard work I am sure it will grow, unfortuantely I am not in your position where I can send email's to companies. I have spent a tidy sum (although saved a fortune doing my own adverts/designs of) in advertising in local rags, magazine and I have walked a few mile handing out flyers. Hey, it's working as people are noticing my brand, more than I expected if honest as for 1000 flyers, 10 people will look, 3 inquire so they say!
By the way, please say what you offer here and maybe you may get some takers!
Chris