The best place to start as a freelancer is by working for your old company as a freelancer or for your old company's clients.
You'll be surprised by how much it is personal relationships that are important, and not necessarily results, though obviously everything counts.
There's a huge business in consulting, and domain specific knowledge is something that can be hard to pick up unless you go in with an existing outfit.
I think the best advice I could give a new graduate is to do your best to join a big consulting company. You'll learn a bunch of things. The money can be pretty good, and the lifestyle can be fun if you are young enough.