Okay, here's how you find clients.
1. Know some narrow segment of businesses well enough to have an idea what problems they're facing and how it translates to dollars, or do enough research to learn same.
2. Track down people matching that segment and pitch them. Use your existing connections if you have them, make connections or go cold if you don't. You will spend enormous effort making new connections either way, so having connections to start with isn't the long-term advantage it might seem.
Note: this requires sales skills. If that's a problem, consulting may not be for you - at least, not as an independent. One of the key selling points of an agency is having the principals deal with much of the lead generation, sales, reputation building, and so forth.
But seriously, if you want to start, start. Stop worrying that you'll be bad at it at first - because you will be, no longer how long you worry about it. And at the same time, they're hiring you because they expect to get value from it.
Go out, make a fool of yourself in front of a few prospective clients, learn stuff in so doing, then do a better job pitching the next few.
If you're half decent at public speaking, see posts by patio11 & bdunn re: throwing events related to the topic you consult on. Being the person in the front of the room at a professional event automatically positions you as an authority figure. If you're terrible at public speaking, this still mostly works if you run the event but invite other people to give the actual talks.