Best way is to contact the head of sales/marketing department and present your proposal. Second option is through mutual connections if you have. I would say go ahead and try. I suggest you practice your pitch before you call.

You need to get yourself notices and build your credibility and network. Work for some time in a consulting agency to get experience and contacts. You can contact companies, ask them what their biggest problems are and give them idea how you would solve it. It's not easy to get clients so prepare to tell in less than a minute why you're better than the one they use at the moment.

Hi, you can approach the head of IT department by email or phone. I suggest you practice your sales pitch first. You don't have much time (about a minute or two) to convince them that you're different and better than others. You may want to check what your competitors offer and promise before you contact any company.