I am a university professor (quantitative sociology) and I am interested in finding consulting gigs, especially for the summer since I'm on 9-month, but possibly year round if just for a few hours/week. Any advice how to find gigs?
What you need to do is establish visibility, especially with those who might benefit from your services. Having an extensive and helpful web site can help, especially if it is, itself, visible, such as one hosted by the university. Perhaps a professional blog or such will give some people an idea of what you can offer. But make it helpful to readers, not just an ad for your services.
But that isn't enough.
One possibility is to make contacts through adult students (MS, and doctoral level). Some of them may be employed by firms that would be interested. But you need to meet the people responsible.
One way to meet people is to do a bit of research on the interests and expertise of people with some authority at local companies/agencies and invite them as guest speakers, either in your own classes or generally.
If you want to cast a wider net, you can use professional meetings to make contacts with others of similar skills and desires and find a way to share contacts. Not a quick process, but it can build visibility.
Another way, not especially lucrative, but possibly rewarding, is to volunteer your expertise to local non-profit or government agencies. I suspect a number of them would be interested in knowing more about their clients. You can also get some of your students involved in this work, to their advantage, perhaps. But this sort of thing will also raise your visibility once it becomes known what you can do.
You can also, of course, form a formal group with colleagues and advertise your services.