I've heard some folks find ways to get in aggressively, while others talk about networking and "staying on the radar" until the big company choses you (because you were friendly and stayed in touch meaningfully on LinkedIn or something along those lines).
Ha!... Who would give away the big secret?!:)
In my experience the key is to stay in touch and check in periodically, both personally and professionally with your lead contacts. Especially former clients that were happy with your work. Ask them if they could use you again or refer to their colleagues/peers... Stay on the radar also helps but I do it by participating in conferences, presenting and networking. If you are considered an opinion leader in your topic - people will be asking for help and advise.
Another quick advise - always leave extra value "on the table" and be generous in your own referrals....
I'd be happy to discuss other tricks of the trade if you are interested.