I recommend starting with twitter. There are some reasons that come to mind first:
• It doesn’t require a lot of resources – other social media sites require more visuals and take more time to understand how they work
• It’s easy to start conversation and to speak up to people who you want to be connected with
• It’ll give the feeling how the social media works and a lot of principles you’ll learn along the way
Set up your account, upload your logo as profile picture, fill in all the data, enter your website address and make sure that you bio makes clear who you are and what you do.
Now, follow some people who are relevant to your business, but don’t overdo this. Preferably, you should follow all the opinion leaders of your niche, some clients you know and partners. At first, when no one is following you, you shouldn’t follow more than 50 people.
Connecting to people on twitter and establishing relationships on web is the same as in real life. Starting off with a story about how great you are probably isn’t the best way. If you act politely, provide help, add value to conversations and generally are a nice person (brand, in this case) others will speak kindly of you. And that’s the goal. That’s why you should try to connect only to people who are relevant to your business. If you will convince them that you are what you say you are and gain credibility (and maintain it), the people who trust you will pass this trust to the ones who trust these influencers.
Simple as that. Help others and prove that you are worth doing business with.