"I think most businesses have a very particular need that I could help meet as a consultant..."

Why do you think this?

Do you know of the companies that have this need? If so, they're the first on your list for you to network into.

Promote yourself: @corin_29 is right. Get LinkedIn endorsements but more than that, consider starting a blog and putting advice on there others can use. If people find and read it and think it's useful, you have a new vehicle to tell people you're available.